How many 5-card poker hands with 2 queens and 3 aces are there?

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Answer 1 · 2018-02-01T13:30:48

24

We want specifically 2 queens and 3 aces.

There are 4 queens in a deck of cards and we want 2 of them (we don't care in what order and so we use the combination formula):

#C_(n,k)=(n!)/((k!)(n-k)!)# with #n="population", k="picks"#

#C_(4,2)=(4!)/((2!)(2!))=24/(2xx2)=6#

And we want 3 aces:

#C_(4,3)=(4!)/((3!)(1!))=4#

Which means there are #6xx4=24# possible hands with this makeup.