AMC8 2003 8, Problem 12

When a fair six-sided dice is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the  faces that can be seen is divisible by $6$?

Solution: We have six cases: each different case, every one where a different number cannot be seen. The rolls that omit numbers one through five are all something times six: an example would be where the number you cannot see is one, so the product should be 2 x 3 x 4 x 5 x 6, and so product should be divisible by six. The roll that omits six on the other hand is 1 x 2 x 3 x 4 x 5, which has 2 x 3, also equal to six. We can see that all of them have a factor of 6 and therefore are divisible by six, so the solution should be E,1. $\fbox{1}$.

Answer: 1