Game of poker Discrete Math

Question

Here is my attempt at solving these questions:

Ok so since there is 52 cards in total and 5 in a hand $52 \choose 5$=2,598,960.

I'm not sure how to solve this. Any help would be great!

Answer 1

First choose one of the 13 ranks for the 3 of a kind cards, next choose 3 of the 4 cards from that rank. Next choose two more ranks for the individual cards and then choose 1 of the 4 for each of the other two ranks. In this way you get $\binom {13} 1\binom 4 3\binom {12} 2\binom 4 1\binom 4 1$.

Alternatively, choose two of the 13 ranks for the 1 of a kind cards first, then choose one of each of the two ranks, then choose one of the remaining 11 ranks for the 3 of a kind cards, and choose 3 of the 4 cards from that rank. $\binom {13} 2\binom 4 1\binom 4 1\binom {11} 1\binom 4 3$.