A poker hand consists of five cards selected at random from a standard 52-card d

Question

A poker hand consists of five cards selected at random from a standard 52-card deck. Find the number of poker hands of each of the following types.

A. Flush: five cards from the same suit

B. Straight Flush: five consecutive cards from the same suits, allowing an ace to be counted as either high (after king) or low (as a 1).

C. Four of a kind, plus a fifth card.

D. Full house: three of one kind and two of another

E. Three of a kind, but not a full house or four of a kind.

F. Straight: five consecutive cards, not necessarily from one suit.

Explanation / Answer

a) 4c1 * 13C5

b) 4 * 9

c) 13c1 * 4C3 * 12C1 * 4C2

d) 13C1 * 4C3 * ( 48C2 - 12C1 *4C2 )

e) 9 * ( 4^5 )

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