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.”

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

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

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

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.)

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?

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

There are 13 cards in a suit, we choose 5 of them, and order does not matter. There are 13C5 = 1287 ways to do this.

As there are 4 suits, then there are 1287*4 = 5148 ways to get all 5 with the same suit.

There are 10 straight flushes/royal flush per suit. There are 4 suits. Thus, there are 10*4 = 40 straight/royal flushes.

Thus, ignoring straight/royal flushes, the number of ways to get 5 with the same suit is

=5148 - 40

= 5108 ways [ANSWER]

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