SOLUTION: What is the probability that I get at least 3 aces from a hand of 5 cards in a deck of 52 cards ?

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Question 1175373: What is the probability that I get at least 3 aces from a hand of 5 cards in a deck of 52 cards ?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Case 1.  The hand contains 3 aces and 2 non-aces.

There are 4 aces in the deck so there are C(4,3) = 4 ways to pick the 3 aces.
There are 48 non-aces in the deck, so you can pick the two non-aces
C(48,2)=1128 ways.
That's C(4,3)C(48,2) = (4)(1128) = 4512 ways.

Case 2.  The hand contains all 4 aces and 1 non-ace.

There are 4 aces in the deck so there is C(4,4) = 1 way to pick all 4 aces.
There are 48 non-aces in the deck, so you can pick the one non-ace C(48,1) = 48
ways.
That's C(4,4)C(48,1) = (1)(48) = 48 ways.

Add them together: 4512+48 = 4560 ways.

Edwin
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