The game of poker involves dealing hands of 5 cards from a standard pack of 52 = 4 13 cards. Order is not important, and we will suppose that just the first hand is dealt.

(a) How many distinct hands are possible?

Find the probability of obtaining a hand with the following features from a randomly shuffled pack:

(b) Three of the cards have the same value, the remaining two are different.

(c) Five values in sequence (Ace = 1).

(d) Five consecutive values in the same suit.