Answer
C(12,1)C(4,2)C(11,3)C(4,1)C(4,1)C(4,1)
Work Step by Step
STEP 1 : select a denomination (not Aces, so 12 to choose from) ...C(12,1)
STEP 2 : select 2 (out of 4 cards of that denomination) ...C(4,2)
STEP 3 : select 3 different denominations from the remaining 11 ... C(11,3)
STEP 4 : select 1 card of the 1st denomination chosen in (3) ...C(4,1)
STEP 5 : select 1 card of the 2nd denomination chosen in (3)...C(4,1)
STEP 6 : select 1 card of the 3rd denomination chosen in (3) ...C(4,1)
TOTAL: (multiplication principle) = C(12,1)C(4,2)C(11,3)C(4,1)C(4,1)C(4,1)