Problem:
For a positive integer n, the factorial notation n! represents the product of the integers from n to 1. For example:
6!=6×5×4×3×2×1
What value of N satisfies the following equation?
5!×9!=12×N!
Answer Choices:
A. 10
B. 11
C. 12
D. 13
E. 14
Solution:
The given equation implies that
N!=125!⋅9!=12(5⋅4⋅3⋅2⋅1)⋅(9!)=10⋅9!=10!,
so N=10.
Answer: A.
The problems on this page are the property of the MAA's American Mathematics Competitions