If you remove all of the jacks, queens, and kings from a 52-card deck, you will be left with a 40-card deck consisting only of aces and cards with ranks 2 through 10.
There are 40 choices for the first card in the hand, 39 choices for the second card (since one card has already been chosen), and 38 choices for the third card, for a total of 403938 = 60,480 unique three-card hands.