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If nP3 = 210, find the value of n.

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nP3 = 210

∴ \(\frac{n!}{(n−3)!}\) = 210

∴ \(\frac{n(n−1)(n−2)(n−3)!}{(n−3)!}\) = 210

∴ (n – 1)(n – 2)(n – 3) = 210

∴ (n – 1)(n – 2)(n – 3) = 7 × 6 × 5

= 7(7 – 1)(7 – 2)

∴ n = 7. Hence, n = 7

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