Question 1058578
There are 4 Aces in the deck, and 52 - 4 = 48 cards which are not Aces.


A five card hand that contains 3 Aces will contain 2 non-Aces.


The number of possible 5-card hands with 3 Aces is:


C(4, 3) * C(48, 2) = {{{(4!/3!(4-3)!)(48!/2!(48-2)!)}}} = 4 * 1128 = 4512 hands


The number of possible 5-card hands of any combination is:


C(52, 5) = {{{52! / 5!(52 - 5)!}}} = 2598960 hands


The probability of a hand with 3 Aces is then:


P(3 Aces) = 4512 / 2598960 = 94 / 54145 ≈ 0.001736