Question

Roberto wants to display his 18 sports cards in an album. Some hold 2 cards and others hold 3 cards. How many different ways can Roberto display his figures?

Answer 1

3 is an odd number, so we need an even number of sets of 3 cards because 18 is an even number.
So we need 0, 2, 4 or 6 sets of three.
0 2-card + 6 3-card, 3 2-card+4 3-card, 6 2-card+2 3-card, 9 2-card+0 3-card. There are only 4 combinations:
(2-card, 3-card)=(0,6), (3,4), (6,2), (9,0).