Three friends are playing draw poker, where each is dealt five cards, and bets o
ID: 3438425 • Letter: T
Question
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?
Explanation / Answer
a.
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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