2024 AMC 12B Problem 2 — Solution | LIVE by Po-Shen Loh

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2024 AMC 12B Problem 2

Attempt Problem 2 of the 2024 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

2.

What is $10! - 7! \cdot 6!?$

$-120$

$0$

$120$

$600$

$720$

Answer: B

Concepts:factorial

Difficulty rating: 1020

Solution:

Note that $6! = 720 = 8 \cdot 9 \cdot 10.$ Therefore $7! \cdot 6! = 7! \cdot (8 \cdot 9 \cdot 10) = 10!.$ So $10! - 7! \cdot 6! = 10! - 10! = 0.$

Thus, the correct answer is B.

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Problem 2 in Other Years

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