# Probability

Compute the probability of randomly drawing five cards from a deck and getting 3 Aces and 2 Kings. (Give your answer as a fraction.)

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3. 👁 95
1. first ace 4/54
second ace 3/53
third ace 2/52
first king 4/51
second king 3/50

multiply them

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posted by Damon
2. Damon's answer represents the prob of the particular order of AAAKK
but it could have been AKAKA, etc
that is, we have to multiply his product by 5!/(2!3!)

btw, there are 52 cards in a deck, not 54
so his product is 4/52 x 3/51 x ....
Once changed to that and multiplied by 5!/(2!3!) you do get
1/108290

or

prob(3 A's and 2K's)
= C(4,3) x C(4,2)/C(52,5)
= 4(6)/2598960
= 1/108290

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posted by Reiny

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