Given nP3 = 9240, find n. (Recall nP3 = n * (n − 1) * (n − 2) for integers n ≥ 3.)

Introduction / Context:Here we invert a cubic-like product n(n − 1)(n − 2). Trying nearby integers quickly identifies the exact match.

Given Data / Assumptions:

• nP3 = 9240.
• nP3 = n(n − 1)(n − 2).

Concept / Approach:Test n = 22 because 222120 seems close to 9240; compute and confirm.

Step-by-Step Solution:

Verification / Alternative check:n = 21 gives 212019 = 7980; n = 23 gives 232221 = 10626, so 22 is correct.

Why Other Options Are Wrong:20, 21, 23 do not produce 9240 exactly.

Common Pitfalls:Using combinations instead of permutations; forgetting the product spans three consecutive integers.

Final Answer:22