Question:
Find the number of ways of choosing $4$ face cards from a pack of $52$ playing cards.
Find the number of ways of choosing $4$ face cards from a pack of $52$ playing cards.
Updated On: Jul 6, 2022
- $495$
- $493$
- $490$
- $492$
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The Correct Option is A
Solution and Explanation
There are $12$ face cards and $4$ are to be selected out of these $12$ cards. This can be done in $^{12}C_{4}$ ways.
Therefore, the required number of ways $= \frac{12!}{4! 8!}= 495$.
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Notes on permutations and combinations
Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.