Question:

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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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.