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

Answer 1

first ace 4/54
second ace 3/53
third ace 2/52
first king 4/51
second king 3/50

multiply them

Answer 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