5.a) Consider the process of choosing the 5-card poker hand containing a 4 of a kind in two steps:
In the first step there are 13 denominations to choose from and this step will result in 4 of the cards being choosen. In the second step there are 48 cards left to choose from (since 4 have already been used).
Since these two steps are independent of each other, you can multiply the possible choices at each step together.
Hence there are 13 · 48 = 624 possible 5-card poker hands which contain a 4 of a kind.