2016 AMC 12A Problem 1

Below is the professionally curated solution for Problem 1 of the 2016 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 12A solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:factorialfactoring

Difficulty rating: 920

1.

What is the value of 11!10!9!?\dfrac{11!-10!}{9!}?

9999

100100

110110

121121

132132

Solution:

Factoring the numerator gives 11!10!9!=10!(111)9!=109!109!=100. \dfrac{11!-10!}{9!}=\dfrac{10!(11-1)}{9!}=\dfrac{10\cdot 9!\cdot 10}{9!}=100.

Thus, the correct answer is B.

Problem 1 in Other Years