Three friends are playing draw poker, where each is dealt five cards, and bets o
ID: 3438376 • Letter: T
Question
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?
Explanation / Answer
A.
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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