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2021 GMC 10B Problems/Problem 1

Problem

What is $5!-4!+3!-2!+1!-0!?$

$\textbf{(A)} ~99 \qquad\textbf{(B)} ~100 \qquad\textbf{(C)} ~101 \qquad\textbf{(D)} ~102 \qquad\textbf{(E)} ~103$

Solution

\begin{align*} 5!-4!+3!-2!+1!-0! &= 120 - 24 + 6 - 2 + 1 -1 \\ &= \boxed{\textbf{(B)}~100} \end{align*} ~pineconee

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