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2016 AMC 10A Problem 1

Problem 1 of 25EasierAlgebraCounting & Probability

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

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Solution

We can factor a 9!9! out of the numerator and simplify. 9!(11⋅10−10)9!=11⋅10−10=110−10=100.\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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Concepts: factorial · factoring

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