- #1
toothpaste666
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Homework Statement
How many 10-card hands are there chosen from a standard 52-card deck in which there are exactly two 4-of-a-kinds; no pairs or 3-of-a-kinds?
The Attempt at a Solution
if there are exactly 2 4 of a kinds that takes up 8 of the 10 cards in the hand and the remaining 2 must be of different kinds since there are no pairs. first we choose 2 kinds for the 4 of a kinds: 13C2 ways . now we have to make sure the last 2 cards are of different kinds so we pick 2 of the remaining 11 kinds: 11C2 ways. now for each of these kinds there are 4 ways to pick a card from them so 4x4 = 16.
the whole process is:
(13C2)(11C2)(16)
is this correct? I want to make sure I am not double counting anything