Three friends are playing draw poker where each is dealt fiv

Three friends are playing draw poker, where each is dealt five cards, and bets on who has the “best hand.” (show work)

A. How many 5-card hands contain all the same suit, regardless of suit (Flush; ignore Straight/Royal Flushes)?

B. How many 5-card hands contain 3 of one rank (2-10, J, Q, K or A), and two of another (Full House)?

C. What is the probability of each hand? (First: how many 5-card hands are there in all?)

D. If two players show a Flush and a Full House, who wins the pot? (A lower probability hand is better than a high probability hand.)

E. How many 5-card hands contain 2 of one rank, and the other three different from the others (One Pair)? Would this beat the others, or not?

For each suit, there are 13 cards.

Thus, there are 13C5 = 1287 such hands per suit.

As there are 4 suits, there are 1287*4 = 5148 such hands in a deck.

Ignoring straight/royal flushes, as there are 10 such per suit, then there are 40 straight/royal flushes.

Thus, there are 5148 - 40 = 5108 [ANSWER]

such hands.

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