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2016 AMC 12A Problem 1

Problem 1 of 25EasierAlgebraCounting & Probability

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

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Solution

Factoring the numerator gives 11!−10!9!=10!(11−1)9!=10⋅9!⋅109!=100. \begin{gathered} \dfrac{11!-10!}{9!}\\ =\dfrac{10!(11-1)}{9!}\\ =\dfrac{10\cdot 9!\cdot 10}{9!}\\ =100. \end{gathered} Thus, the correct answer is B.

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Concepts: factorial · factoring

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.