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  4. Find the number of ways of choosing 4 face cards from a pack of 52 playing cards.

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Q. Find the number of ways of choosing $4$ face cards from a pack of $52$ playing cards.

Permutations and Combinations

Solution:

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 $= \frac{12!}{4! 8!}= 495$.