1996 AMC 12 Problem 3

Attempt Problem 3 of the 1996 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1996 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

\displaystyle\frac{(3!)!}{3!}=

1

2

6

40

120

Evaluate the inner factorial before the outer factorial

Cancel the denominator from the product in the numerator

Since

3!=6,

the expression is

\frac{6!}{6}=5!=120.

Thus the correct answer is E.

Problem 3 in other years