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

2016 AMC 10A Problem 1 — Solution

2016 AMC 10A Problem 1

Attempt Problem 1 of the 2016 AMC 10A 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 2016 AMC 10A solutions, or check the answer key.

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

$99$

$100$

$110$

$121$

$132$

Answer: B

Concepts:factorial factoring

Difficulty rating: 560

Solution:

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 .

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