What is 10! - 7! × 6!?

2024 AMC 10B Problem 2 — Solution

2024 AMC 10B Problem 2

Attempt Problem 2 of the 2024 AMC 10B 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 10B solutions, or check the answer key.

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

$-120$

$0$

$120$

$600$

$720$

Answer: B

Concepts:factorial

Difficulty rating: 980

Solution:

Write $10! = 10 \cdot 9 \cdot 8 \cdot 7! = 720 \cdot 7!.$ But $720 = 6!$ too, so $10! = 6! \cdot 7! = 7! \cdot 6!.$ The two terms are the same. That makes $10! - 7! \cdot 6! = 0.$ Therefore, the answer is B.

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