| There are 5 cards: a b c d e
How many 5 card arrangements can be made if card c cannot be on either end
c cannot be at either end, so for slot a there are 4 possibilites (all the cards except c)
now go to the other end (slot e) - there are 3 possibilites because one of them was used up on the first slot
now go back to slot b - there are 3 possibilities - all 5 cards minus the 2 that are already placed at either end
2 possibilites for slot c
1 possibility for slot d
so there are 4 x 3 x 2 x 1 x 3 = 72 different arrangements. |