Question

A standard deck of cards has 13 cards for each of the 4 suits, with that in mind how many hands of 5 cards involve exactly 2 suits

Answer 1

To find the number of hands of 5 cards involving exactly 2 suits, we need to consider the number of ways to choose 2 suits and then choose cards from those suits. The total number of hands with exactly 2 suits is 146,304.

Step-by-step explanation:

To find the number of hands of 5 cards involving exactly 2 suits, we need to consider the number of ways to choose 2 out of the 4 suits and then choose 2 cards from each of those suits, and finally choose the last card from any suit.

First, we use combinations to select 2 suits out of 4, which can be done in C(4, 2) = 6 ways. Then we choose 2 cards from each of those 2 suits, which can be done in C(13, 2) * C(13, 2) = 78 * 78 = 6084 ways.

Finally, we choose the last card from any of the 4 suits, which can be done in 4 ways.

So, the total number of hands of 5 cards involving exactly 2 suits is 6 * 6084 * 4 = 146,304