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2024 AMC 10BProblem 2P1-10~1 minPrint
Algebraic ManipulationDivisibility & FactorsUse the answer choices (mod checks, size, form) to eliminate or selectSet up the equation/formula and compute; no special trick needed

What is 10!−7!⋅6!10! - 7! \cdot 6!

(A) −120(B) 0(C) 120(D) 600(E) 720\textbf{(A) } -120 \qquad\textbf{(B) } 0 \qquad\textbf{(C) } 120 \qquad\textbf{(D) } 600 \qquad\textbf{(E) } 720

[ONLY FOR CERTAIN CHINESE TESTPAPERS]

What is 10!−7!⋅6!−5!10! - 7! \cdot 6! - 5!

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2024 12B #2.