Use the multiplication principle to tell the total number of three card hands (permutations ) that can be made with two aces?

To form a three-card hand that includes two aces, we first select 2 aces from the available 4 aces in a standard deck, which can be done in ( \binom{4}{2} = 6 ) ways. The third card can be any of the remaining 48 cards (52 total cards minus the 4 aces). Thus, the total number of three-card hands with two aces is ( 6 \times 48 = 288 ).