1.How many different 5-card hands contain exactly 4 spades? 2.How many different 5-card hands contain exactly 4 cards of the same suit? 3.How many diff. 5-card hands contain cards of exactly one suit?

Answer 1

There are 13 cards in each of 4 suits, so there are 13 spades, and 52-13 = 39 non-spades

Thus, the number of 5 card hands with 4 spades is the number of hands with 4 spades and 1 non-spade =

C(13,4) * C(39,1) = 715 * 39 = 27885

4 * the answer from 1 for the 4 suits equals 4 * 27885 = 111540

4 * C(13,5) = 4 * 1287 = 5148