A hand is a set of five cards chosen from a standard deck of cards (see Exercise 7(b))....

A hand is a set of five cards chosen from a standard deck of cards (see Exercise 7(b)).

Determine the number of hands in which

(a) all five cards are in the same suit (a flush).

(b) two cards have the same rank and the other cards have different ranks (a pair).

(c) two cards have the same rank, two other cards have the same rank different from the first pair, and the remaining card has another different rank (two pairs).

(d) three cards have the same rank and the other two cards have different ranks (three of a kind).

(e) all cards are in consecutive ranks (a straight). The A is considered the lowest rank of 5, 4, 3, 2, A and the highest rank of A, K, Q, J, 10. Include in your count hands that are also flushes.

Reference : Exercise 7 (b)