What is the value of (11!-10!)/(9!)?

2016 AMC 10A Problem 1

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What is the value of

\dfrac{11!-10!}{9!}?

99

100

110

121

132

Factor

10!

9!

from the numerator

Use

11!=11\cdot10\cdot9!

We can factor a

9!

out of the numerator and simplify.

\begin{aligned} \dfrac{9!(11 \cdot 10 - 10)}{9!} &=11 \cdot 10 - 10 \\&= 110 - 10 \\&= 100. \end{aligned}

Thus, the correct answer is B .