SOLUTION: if a 5 card poker hand is dealt with a well-shuffled deck of 52 cards what is the probability of being dealt two pairs?
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Question 1113210: if a 5 card poker hand is dealt with a well-shuffled deck of 52 cards what is the probability of being dealt two pairs? Answer by math_helper(2461) (Show Source):
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There are 13 ranks (values) and 4 different suits for each rank.
To get two pairs there are quite a few combinations involved:
13C2 ways to get two different card ranks that will become the two pairs
4C2 ways to get the two suits for one of the pairs
4C2 ways to get the two suits for the other pair
11C1 ways to get the card (rank) that matches neither of the paired cards
4C1 ways to get the card (suit) that matches neither of the paired cards
These must be multiplied:
(13C2)*(4C2)*(4C2)*(11C1)*(4C1) = (13*12/2)*(6)*(6)*(11)*(4) = 123552 two-pair hands
There are 52C5 poker hands. Divide 123552 by 52C5 to get the probability (it is a little less than 5%).
