Problem:
When a fair six-sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the numbers on the five faces that can be seen is divisible by
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If is one of the visible faces, the product will be divisible by . If is not visible, the product of the visible faces will be , which is also divisible by . Because the product is always divisible by , the probability is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions