2016 AMC 12A Problems/Problem 1

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Problem

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

$\textbf{(A)}\ 99\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 110\qquad\textbf{(D)}\ 121\qquad\textbf{(E)}\ 132$

Solution

\[\frac{11!-10!}{9!} = \frac{11!}{9!} - \frac{10!}{9!}\] \[\frac{11\cdot 10\cdot 9!}{9!} - \frac{10\cdot 9!}{9!}\] \[(11\cdot 10) - 10\] \[\boxed{\textbf{(b) } \, 100}\]

See Also

2016 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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All AMC 12 Problems and Solutions

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