Determine the number of 5-card combinations out of a deck of 52 cards if there is exactly one ace in each combination. By fundamental principle of counting, The required number of ways = ⁴C₁ × ⁴⁸C₄ = (4!) / [1!STEP 2 : Finding the number of ways in which 5 card combinations can be selected. Number of cards in a deck = 52. How many ways are there to select 47 cards from a deck of 52 cards? The different ways to select 47cards from 52 is. Find the number of $5$-card hands where all $4$ suits are present. Here’s how to use it: Number of Items: Enter the total number of items in the set. Using our combination calculator, you can calculate that there are 2,598,960 such. The COMBIN function in Excel is also known as the combination function as it calculates the number of possible combinations for two given numbers. Take 3 letters a, b, and c. I. , 13 hearts and 13 diamonds. Unit 8 Counting, permutations, and combinations. 4, 6 Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in. A poker hand consists of 5 cards randomly drawn from a deck of 52 cards. In a deck, there is 4 ace out of 52 cards. Question From - NCERT Maths Class 11 Chapter 7 EXERCISE 7. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. {52 choose n}$ represents all possible combinations of n cards. (A poker hans consists of 5 5 cards dealt in any order. )Refer to Example 9. It's got me stumped for the moment. If we sum the preceding numbers, we obtain 2,598,960 and we can be confident the numbers are correct. In a deck of 52 cards, there are 4 aces. Your answer of 52 × 51 for ordered. This number will go in the denominator of our probability formula, since it is the number of possible outcomes. (a) a telephone number. Statistics Probability Combinations and Permutations. - 36! is the number of ways 36 cards can be arranged. a) Four cards are dealt, one at a time, off the top of a well-shuffled deck. This is the number of full houses we can draw in a game of 5-card poker. 3 2 6 8. Solve Study Textbooks Guides. The observation that in a deck of. com We need to determine how many different combinations there are: \begin {aligned} C (12,5) &= \frac {12!} {5! \cdot (12-5)!} \\ &= \frac {12!} {5! \cdot 7!} = 792 \end {aligned} C (12,5) = 5! ⋅ (12 − 5)!12! = 5! ⋅ 7!12! = 792. In how many of these (iii) are face cards, King Queen and Jack are face cards Number of face cards in One suit = 3 Total number of face cards = Number of face cards in 4 suits = 4 × 3 = 12 Hence, n = 12 Number of card to be selected = 4 So, r = 4 Required no of ways choosing face cards = 12C4 = 12!/4!(12 − 4)!Finding Combinations: Finding the number of combinations using a set number of options depends on whether we are allowed to repeat an option or if each part of the combination must be unique. View Solution. There are 52 - 4 = 48 non-aces. 4. Find how many combinations of : 3 cards of equal face values and 2 cards of different values. Once everyone has paid the ante or the blinds, each player receives five cards face down. Determine the number of 5-card combinations out of a deck of 52 cards if there is exactly one ace in each combination. Exactly 1 ace out of 4 aces can be selected in ⁴C₁ ways. ⇒ C 1 4 × C 4 48. Thus, by multiplication principle, required number of 5 card combinations5 card poker hand combination a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter n P r = n!/r!(n - r)! factorial The product of an integer and all the integers below it probability the likelihood of an event happening. Find the probability of getting an ace. ⇒ C 1 4 × C 4 48. Divide the factorial of the total by the denominator, as described above: 3,628,800/17,280. 1. A combination of 5 cards have to be made in which there is exactly one ace. asked Dec 30, 2016 in Mathematics by sforrest072 (130k points) permutations and combinations; combinations; 0. ${13 choose n}$ represents drawing n cards of different. The 11 Best Credit Card Combinations – Amex, Chase, Citi, Capital One [November 2023] Stephen Au Updated: November 14, 2023, 12:59pm CST. number of ways selecting one ace from 4 aces = ⁴C₁ number of ways selecting 4 cards from 48 cards = ⁴⁸C₄ now, A/C to concept of fundamental principle of counting, 5 cards with exactly one ace can be selected in ⁴C₁ × ⁴⁸C₄ ways. Open in App. Total number of cards to be selected = 5 (among which 1 (king) is already selected). Odds can then be expressed as 5 : 8 - the ratio of favorable to unfavorable outcomes. We are given 10 cards, the first 5 are the current hand, and the second 5 are the next five cards in the deck. Ways of selecting the remaining 4 cards from 48 cards= 48 C 4The number of combinations of n different things taken r at a time is given by. Combination can be used to find the number of ways in which 7 hand cards can be chosen from a set of 52 card decks as the order is not specified. View Solution. Player 1's Best Hand is: A A Q Q 8 8 6 6 5 5. Problem 3 : Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination. You. So ABC would be one permutation and ACB would be another, for example. The combination formula is used. Solution. For the numerator, we need the number of ways to draw one Ace and four other cards (none of them Aces) from the deck. number of ways selecting one ace from 4 aces = ⁴C₁ number of ways selecting 4 cards from 48 cards = ⁴⁸C₄ now, A/C to concept of fundamental principle of counting, 5 cards with exactly one. This is a selection. The total number of combinations would be 2^7 = 128. Class 11 Engineering. ”In general, if there are n objects available from which to select, and permutations (P). by Maths experts to help you in doubts & scoring excellent marks in Class 11 exams. 20%. SEE MORE TEXTBOOKS. The observation that in a deck of 52 cards we have 4 kings and 48 non kings. Determine the number of 5-card combinations out. Solve Study Textbooks Guides. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. For example: Player 1: A A 6 6. The probability of drawing the 4th one is 1/33. The State of Climate Action 2023 provides the world’s most comprehensive roadmap of how to close the gap in climate action across sectors to limit global warming. A card is selected from a standard deck of 52 playing cards. 7k points) permutations and combinations; class-11 +5 votes. In order to find the actual number of choices we take the number of possible permutations and divide by 6 to arrive at the actual answer: 7C3 = 7P3 3! = 7! 4! ∗ 3! In a combination in which the order is not. Now can you calculate the number with at least two kings? $endgroup$ –To find the number of ways to select 3 of the 4 paintings, disregarding the order of the paintings, divide the number of permutations by the number of ways to order 3 paintings. 05:01. Transcript. Find your r and n values by choosing a smaller set of items from a larger set. ,89; 4. Therefore, to calculate the number of combinations of 3 people (or letters) from a set of six, you need to divide 6!. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. A permutation is an ordered arrangement. Combinations 10,200: A Straight is five cards in numerical order, but not in the same suit. Answers 2. Thus, the required number of 5 card combinationsGenerated 4 combinations. This approach indicates that there are 10 possible combinations of 5 cards taken 2 at a time. As there should be exactly one king in each combination of 5 cards, thus one king can be selected as a combination of 4 kings taken 1 at a time. Q2. Insert the numbers in place of variables in your formula and calculate the result. ,89; 3. Win the pot if everyone else folds or if you have the best hand. GRE On-Demand. In Combinations ABC is the same as ACB because you are combining the same letters (or people). The remaining percentage consists. 9. Thus the number of ways of selecting the cards is the combination of 48 cards taken 4 at a time. All we care is which five cards can be found in a hand. Determine the number of 4 card combinations out of a deck of 52 cards if there is no ace in each combination. For each of the above “Number of Combinations”, we divide by this number to get the probability of being dealt any particular hand. The following exercises deal with our version of the game blackjack. Join / Login >> Class 11 >> Maths >> Permutations and Combinations. Q. There are 52 cards in a poker deck, and a hand is a combination of 5 of those cards. Now, there are 6 (3 factorial) permutations of ABC. Question 5: Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls, and 7 blue. Find how many combinations of : 3 cards of equal face values and 2 cards of different values. A combination of 5 cards have to be made in which there is exactly one ace. Class 7. Let’s enter these numbers into the equation: 69 C 5 = 11,238,513. Probability and Poker. Solution 1 (Correct): We choose 2 ranks out of 13, which can be done in (132) ( 13 2) ways. You can calculate it using the formula C(n,r) = n! / [r!(n-r)!], where 'n' is the number of items to choose from (52 cards in. Given a deck of $52$ cards There are $4\;\;Ace$ cards in a deck of $52\;\;cards. We would like to show you a description here but the site won’t allow us. Thus cards are combinations. Then, one ace can be selected in 4 C 1 ways and the remaining 4 cards can be selected out of the 4 8 cards in 4 8 C 4 ways. ⇒ 778320. , 10, J, Q, K). Straight. 6! 3! = 6 · 5 · 4 · 3! 3! = 6 · 5 · 4 = 120. Solution Verified by Toppr The observation that in a deck of 52 cards we have 4 kings and 48 non kings. A flush consists of five cards which are all of the same suit. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Sorted by: 1. First, determine the combinations of 5 distinct ranks out of the 13. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. View Solution. B. magic filters photo_filter. Generate a standard Poker deck of 52 cards (no Jokers) Shuffle said deck. Determine the number of 5 cards combination out of a deck of 52 cards if at least one of the cards has to be a king. 144 %. Best Citi credit card combo. . The number of ways to choose 5 cards from the 13 cards which are diamonds is ${13 choose 5}$. If we pick 5 cards from a 52 card deck without replacement and the same two sets of 5 cards, but in different orders, are considered different, how many sets of 5 cards are there? Solution. To find the number of ways in which a smaller number of objects can be selected from a larger pool, we use the combination formula. Four of a kind c. Things You Should Know. (r + n -1)! r! × (n - 1)! This free calculator can compute the number of possible permutations and. This can be calculated using the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be chosen. Lastly, we multiply those two quantities to get the probability of drawing 4 cards with 2 aces and 2 kings regardless of arrangement. explanation: think of this top part of the probability (numerator) as 4p4 since you have 4 numbers to pick from and you want to pick 4 numbers, the number of ways. taken from a standard 52 card deck? (using combinations)-----# of possible 5-card hands: 52C5 # of 5-card hands with no kings: 48C5-----Ans: 52C5-48C5 = 2,404,380 ===== Find the number of possible 5 card hands that contain At Most 1 diamond. Hence, there are 1277(4 5-4) = 1,302,540 high card hands. It makes sense, since you don't care about the arrangement of the cards you are not going to have in a 9-card hand. The number of possible 5-card hands is 52 choose 5 or ({52!}/{(5! ullet 47!)} = 2598960). 6 million hands, how many are 2 pair hands?Probability of a full house. This is because 1 or 2 cards are irrelevant in classifying the poker hand. 5 6 4 7. The probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand by the total number of 5-card hands (the sample space, five-card hands). What is the probability that we will select all hearts when selecting 5 cards from a standard 52 card deck? Solution. r-combinations of a set with n distinct elements is denoted by . From a deck of 52 cards, 5 cards combinations have to be made in such a way that in each selection of 5 cards there is exactly 1 king. Determine the number of 5 card combination out of a deck of 52 cards if each selection of 5 cards has at least one king. One card is selected from the remaining cards. After the first card, the numbers showing on the remaining four cards are completely determine. For many experiments, that method just isn’t practical. Take 1 away from that number, multiply those two numbers together and divide by 2. Solution For Determine the number of 5-card combination out of a deck of 52 cards if each selection of 5 cards has exactly one king. In this case, order doesn't matter, so we use the formula for combinations. Alternatively, this is asking for the number of ways to leave behind 47 (52-5) cards in a particular order from the deck box. In general we say that there are n! permutations of n objects. Calculate the number of different 5-card poker hands that make a full house - 3 of a kind plus a pair. 1-on-1 Online Tutoring. Enter a custom list Get Random Combinations. By multiplication principle, the required number of 5 card combinations are. There are total 4 aces in the deck of 52 cards. We refer to this as a permutation of 6 taken 3 at a time. Then, one ace can be selected in ways and the remaining 4 cards can be selected out of the 48 cards in ways. Join / Login. A researcher selects. So the remaining = 5 – 3 = 2 . $ Section 7. And we want to arrange them in unordered groups of 5, so r = 5. Select whether you would like to calculate the number of combinations or the number of permutations using the simple drop-down menu. Paired hands: Find the number of available cards. $ According to question, we need to select $1;;Ace$ card out the $4;;Ace;;cards$Since in the combination of 5 cards, one place is occupied by a king, thus there remain 4 cards and also the total number of cards left is 48 after the removal of 4 kings from 52 cards. We need to select exactly one ace for our combination. We may be compensated when you click on product links, such as credit cards, from one or more of our advertising partners. . To calculate the number of ways to make a four of a kind in a five card poker hand, one could reason as follows. C. In a 5 card poker with a standard 52- card deck, 2, 598, 960 different hands are possible. View Solution. ADVERTISEMENT. ) Straight flush ( not including a royal flush). Question . Selection of 5 cards having at least one king can be made as follows: 1 king and 4 non kings or 2 kings and 3 non - j8li3muee. Selection of 5 cards having at least one king can be made as follows: 1 king and 4 non kings or 2 kings and 3 non kings or 3 kings and 2 non kings or 4 kings and 1 non king. The low card can be chosen in $10$ ways. CBSE Board. Therefore, the number of possible poker hands is \[\binom{52}{5}=2,598,960. 3. There are 4 Ace cards in a deck of 52 cards. these 16 cards, 4 are chosen. Answer and. An Introduction to Thermal PhysicsDaniel V. Then, one ace can be selected in 4C1ways and the remaining 4 cards can be selected out of the 48cards in 48 C4 ways. The last card can be chosen in 44 44 different ways. Find the number of 5 card combination out of a deck of 52 cards if there is exactly one ace in each combination. Then, one ace can be selected in `""^4C_1` ways and the remaining 4 cards can be selected out of the 48 cards in `"^48C_4`ways. Misc 8 Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. In a deck of 52 cards, there are 4 kings. Solve. I. There are also two types of combinations (remember the order does not matter now): Repetition is Allowed: such as coins in your pocket (5,5,5,10,10) No Repetition: such as lottery numbers (2,14,15,27,30,33) 1. Since the order does not matter, this means that each hand is a combination of five cards from a. From a deck of 52 cards, 5-card combinations have to be made in such a way that in each selection of 5 cards, there is exactly one king. Player 2: K K J J. Divide the latter by the former. Question . e. of ways in which the 5 cards can. Cards are dealt in. 1 king can be selected out of 4 kings in `""^4C_1` ways. Publisher: OpenStax. Note that there are four suits, so the number of ways of drawing five cards from the same suit is four times, say, the number of ways of drawing five clubs. (485) (525), ( 48 5) ( 52 5), for we have 48 choose 5 possible hands with no aces. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. Class 5. For the numerator, we need the number of ways to draw one Ace and four other cards (none of them Aces) from the deck. Determine the number of five-card poker hands that can be dealt from a deck of 52 cards. statistics. The probability is the probability of having the hand dealt to you when dealt 5 cards. We are using the principle that N (5 card hands)=N. Then click on 'download' to download all combinations as a txt file. This value is always. By multiplication principle, the required number of 5 card combinations are. 4 3 2 1. Working out hand combinations in poker is simple: Unpaired hands: Multiply the number of available cards. Solution For [Solved] Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination. In general we say that there are n! permutations of n objects. 17. Solution. We are using the principle that N (5 card hands)=N. Let’s deal North’s hand rst. So in all, there are. In Combinations ABC is the same as ACB because you are combining the same letters (or people). c) Two hearts and three diamonds. There are 13 2 di erent ways to choose 2 denominations from the 13 available denominations. Solution. You are "duplicating combinations", because the same king that you choose out of 4 4 kings in one combination, can be chosen out of 51 51 cards in another combination. "To calculate the number of combinations with repetitions, use the following equation. In order to grasp how many card combinations there are in a deck of cards this thorough explanation puts it in terms that we are able to understand. Click on Go, then wait for combinations to load. So, we are left with 48 cards out of 52. Read. Medium. If you want to count the size of the complement set and. The Probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand ( Frequency) by the total number of 5-card hands (the sample space; ( 52 5 ) = 2 , 598 , 960 { extstyle {52 choose 5}=2,598,960}So we say that there are 5 factorial = 5! = 5x4x3x2x1 = 120 ways to arrange five objects. Step by step video, text & image solution for Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. This probability is. Click here👆to get an answer to your question ️ "Determine the number of 5 - card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. You are dealt a hand of five cards from a standard deck of 52 playing cards. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination Solution: The total no. Establish your blinds or antes, deal 5 cards to each player, then bet. of ways of selecting 4 cards from the remaining deck of 48 cards = ⁴⁸C₄. To find the total number of outcomes for two or more events, multiply the number of outcomes for each event together. Edited by: Juan Ruiz. In other words, for a full house P =. a) Three face cards, b) A heart flush (all hearts). C. To refer to the number of cards drawn, I will add the number at the end of the name, for example, If I want to tell the frequency of two pairs in a 5-card hand, I will say 2K2K5. Now if you are going to pick a subset r out of the total number of objects n, like drawing 5 cards from a deck of 52, then a counting process can tell you the number of different ways you can. 71. For the numerator, we need the number of ways to draw one Ace and four other cards (none of them Aces) from the deck. Solution: Given a deck of 52 cards. Determine the number of 5 card combinations out of a deck of 52 cards, if there is exactly one ace in each combination. For the second rank we choose 2 suits out of 4, which can be done in (4 2) ( 4 2) ways. 2. Number of questions must be answered = 2. The first example using combinations is an example of selecting 5 cards at once. Combinations with Repetition. _square]. Determine the number of 5. Previous Question < > Next. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. For the purpose of this table, a royal flush, straight flush, flush, and straight must use all cards. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. A class has to elect 3 members of a committee from 6 candidates. Example [Math Processing Error] 5. means the number of high card hands is 2598960 – 40 – 624 – 3744 – 5108 – 10200 – 54912 – 123552 – 1098240 = 1,302,540. Finally, you can switch between having the results displayed in a field (for copying and pasting) and a. Example [Math Processing Error] 3. The dealer’s cards are dealt with the second card face up, so the order matters; the other players’ hands are dealt entirely face down, so order doesn’t matter. Find the number of 5 card combination out of a deck of 52 cards if there is exactly one ace in each combination. For the number of hands we can draw getting specifically 2 Jacks and 3 Aces, we calculate that this way - we only need to concern ourselves with picking out the number of cards of the 4 available in each of the listed ordinals, and so we get:If the team believes that there are only 10 players that have a chance of being chosen in the top 5, how many different orders could the top 5 be chosen? For this problem we are finding an ordered subset of 5 players (r) from the set of 10 players (n). I worked out in a difference approach. Solution. 1302 ____ 18. And so on. - Maths [Solved] Determine the number of 5 cards combinations out of a deck of 52. Combination and Permutation Calculator. e one ace will be selected from 4 cards and remaining 4 cards will be selected from rest 48 cards . Transcript. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king Solution: The total no. 7842 e. Each of these 2,598,960 hands is equally likely. Count the number that can be classified as four of a kind. . Step by step video & image solution for Determine the number of 5 card combinations out of a deck of 52 cards if at least one of the 5 cards has to be as king? by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams. . Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. From a standard 52-card deck, how many 5-card hands consist entirely of red cards? Solution: There are total 26 red card i. We are given 10 cards, the first 5 are the current hand, and the second 5 are the next five cards in the deck. Therefore, the number of possible poker hands is [inom{52}{5}=2,598,960. . 4) Two cards of one suit, and three of another suit. Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM Expert Answer The observation. This follows from the "multiplication rule": if event A can occur in p ways, and event B can occur in q ways, then the number of ways in which both events A and B can occur is pq. First, we count the number of five-card hands that can be dealt from a standard deck of 52 cards. Given 5 cards Select the first card from 5 possibilities The second card from 4 possibilities The third card from 3 possibilities. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. The combination formula is mathematically expressed as {eq}^nC_r=dfrac{n!}{r!(n-r)!} {/eq}, where {eq}r {/eq} is the number of distinct objects to be selected from {eq}n {/eq} distinct objects. (c) a hand of cards in poker. If more than one player has a flush you award the pot to the player with the highest-value flush card. How many combinations are possible that have at most 1 red card? a. Answer. T T. P (None blue) There are 5 non-blue marbles, therefore. the number of ways of choosing an unordered set of $5$ cards from a $52$-card deck. Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king? Advertisement. For example, a “four of a kind” consists of four cards of the same value and a fifth card of arbitrary. Combination State if each scenario involves a permutation or a combination. Ask doubt. Thus the number of ways of selecting the cards is the combination of 48 cards taken 4 at a time. A 6-card hand. Correct option is C) We need 5 cards so in that exactly three should be ace. 1 answer. This number will go in the denominator of our probability formula, since it is the number of possible outcomes. 4 5 1 2. where,. n} A = { 1, 2, 3,. Since, there is exactly one ace in a combination of 5 cards, so no of ways of selecting one ace = . To determine the number of 5-card hands possible from a deck of cards, you would use the probability concept known as Combinations. 13 × 1 × 48 13 × 1 × 48. \ _\square\] Poker hands are put into classifications so that players can know how much their hand is worth. Whether you use a hand calculator or a computer you should get the number: [Math Processing Error] 1365. ) based on the number of elements, repetition and order of importance. View Solution. Here are the steps to follow when using this combination formula calculator: On the left side, enter the values for the Number of Objects (n) and the Sample Size (r). Probability of getting a flush (and so excluding straight and royal flushes) =5108/2598960~=. Each combination of 3 balls can represent 3! different permutations. Class 6; Class 7; Class 8; Class 9; Class 10; Class 11; Class 12; Other BoardsDecide whether the situation described involves a permutation or a combination of objects. or M = 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 M = 5! = 120 The number of hands in poker is then #hands = 52!A standard $52$-card deck consists of $4$ suits and $13$ ranks. It will list all possible combinations, too! Hence, the number of 5 card combinations out of a deck of 52 cards, if there is exactly one ace in each combination is 778320. We count the number of $5$-card hands that have exactly $1$ card below $8$. Therefore, P( One of each color ) = 3C1 × 2C1 × 3C1 8C3 = 18 56. We have 52 cards in the deck so n = 52. Sorted by: 1. For more information, see permutations - How many ways to select 5 cards with at least one king. Approximately 50% of "poker hands”, a set of 5 cards, have no pair or other special combination of cards, approximately 42% of hands have exactly one pair of same valued cards, and only 2. Number of kings =4 . Hence, using the multiplication principle, required the number of 5 card combinationIt's equivalent to figuring out how many ways to choose 2 cards from a hand of 4 kings (king, king, king, king) to turn into aces; it's simply ₄C₂. Hard. Create Tests & Flashcards. Second method: 4 digits means each digit can contain 0-9 (10 combinations). View Solution. By fundamental principle of counting, The required number of ways = ⁴C₁ × ⁴⁸C₄ = (4!) / [1! STEP 2 : Finding the number of ways in which 5 card combinations can be selected. So 10*10*10*10=10,000. Then the solution to the problem - that is, the probability of at least one ace appearing in a 5-card hand - is one minus the complement:Thus we use combinations to compute the possible number of 5-card hands, (_{52} C_{5}). Combinations sound simpler than permutations, and they are. (e. Number of questions to be answered = 5.