How many five-card hands chosen from a standard deck contain two hearts and three spades?

Answer 1

you are choosing 2 of the 13 hears and 3 of the 13 spades
number = C(13,2) x C(13,3)
= 78(286)
= 22308

in factorial form:
13!/(2!11!) x 13!/(3!10!)
= 13x12/2 x 13x12x11/6
= 22308