What is the probability of getting exactly three aces in a five-card poker hand dealt from an ordinary 52 card deck?

The probability of getting 3 aces in the order AAABB

is; P(AAABB)

=

(4/52)∙(3/51)∙(2/50)∙(48/49)∙(47/48) =

0.0001736...

There are 5C3 =

5!/(3!∙(5-3)!) =

10 different ways in which the aces can come

out.

So the probability of getting exactly three aces in a five card Poker hand dealt

from a 52 card deck is, P(3A)

~ 10∙(0.0001736) ~ 0.001736 ~ 0.1736%