Question:
Find the number of ways of choosing $4$ cards from a pack of $52$ playing cards when cards are of the same colour.
Find the number of ways of choosing $4$ cards from a pack of $52$ playing cards when cards are of the same colour.
Updated On: Jul 6, 2022
- $ 29900 $
- $29925$
- $29910$
- $29920$
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The Correct Option is A
Solution and Explanation
$4$ red cards can be selected out of $26$ red cards
in $^{26}C_{4}$ ways. $4$ black cards can be selected out of $26$ black cards in $^{26 }C_{4}$ ways.
Therefore, the required number of ways $=\,^{26}C_{4} + \,^{26}C_{4}$
= $2 \times \frac{26!}{ 4! 22!} = 29900$.
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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.