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  4. Find the number of ways of choosing two red cards and two black cards from a pack of 52 playing cards.

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Q. Find the number of ways of choosing two red cards and two black cards from a pack of $52$ playing cards.

Permutations and Combinations

Solution:

There are $26$ red cards and $26$ black cards. Therefore, the required number of ways
$=\,{}^{26}C_{2} \times \,{}^{26}C_{2}$
$= \left(\frac{26!}{2!\, 24!}\right)^{2} = \left(325\right)^{2}$
$= 105625$