In a standard deck of cards, there are 13 diamond cards and 39 non diamonds. To choose 3 diamonds from 13 cards would be equivalent to 13*12*11 as there are less cards to choose from each time you remove a card. To choose two non diamonds from the other non diamonds cards would be equivalent to 39*38, taking into account the number of cards you remove each time you pick out one card. Hence the total number of ways is 13x12x11x39x38.
