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If $^{n + 2} C_{3} =^{n + 3} P_{2} - 20$ then $n$ is equal to:

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Correct option is D

16(n+2)(n+1)n=(n+3)(n+2)−20⇒ n3+3n2+2n=6n2+5n+6−120⇒ n3−3n2−28n+84=0⇒ (n−3)n2−28=0As n is a positive integer we get n=3

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If n+2C3=n+3P2−20 then n is equal to:

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If $^{n + 2} C_{3} =^{n + 3} P_{2} - 20$ then $n$ is equal to: