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Hi all
The question is:
Given a 52 card deck, how many hands of 5 cards have
a) exactly 3 aces?
My guess is 4 x 3 x 2 x 48 x 47. Although this is not correct according to my text book.
b) at least 3 aces?
My guess is, having 3 aces plus having 4 aces = (4 x 3 x 2 x 48 x 47) + (4 x 3 x 2 x 1 x 48) . This is also not correct
For part (a) you can modify slightly to get the correct answer.Quote:
Originally Posted by Bushy
(4*3*2)/3! * (48*47)/2!
This is also C(4,3) * C(48,2) where C(n,k) is binomial coefficient.
4*3*2 means order matters; 4*3*2/3! means order does not matter.
For part (b) you can do as you suggested, but you will need to modify your expression for 4 aces.
Hello, Bushy!
Are you familiar with Combinations?
Quote:
Given a 52-card deck, how many hands of 5 cards have:
(a) exactly 3 Aces?
There are 4 Aces and 48 Others.
We want 3 Aces and 2 Others.
. . There are: .ways to get 3 Aces.
. . There are: .ways to get 1 Other.
Therefore: .hands with exactly 3 Aces.
Quote:
(b) at least 3 Aces?
"At least 3 Aces" means: .
3 Aces, 2 Others: from part (a),ways.
4 Aces, 1 Other:
. . . There is: .way to get 4 Aces.
. . There are: .ways to get 1 Other.
Hence, there are: .ways to get 4 Aces, 1 Other.
Therefore: .ways to get at least 3 Aces.