math
posted by kelly on .
hi, could someone please help me solve this problem, i know the answer is 24, i just need to know how to solve it.
a "lucky dollar" is one of nine symbols on each reel of a slot machine with three reels. a player receives one of the various payouts whenever one or more lucky dollars appear in the window of the machine. find the number of winning combinations for which the machine has a payoff.

$ in first slot with 81 possibilities for the next two
$ in the second slot with 8 possibilities in the left slot and 9 in the right slot = 72 (Double counting must be avoided; hence the 8)
$ in the third slot with 8 possibilities in the left slot and 8 in the middle slot = 64.
Total = 81 + 72 + 64 = 217 possible payout combinations (out of 9^3 = 729)