Evaluate n+1Cn-2 If n =15

Evaluate ⁿ⁺¹C_n-2 If n =15

Correct Answer: Option D

Explanation

(frac{n + 1 (n – 2)}{(n + 1)!})
(frac{(n + 1) + (n – 2)!(n – 2)!}{(n + 1)!})
(frac{(n + 1)(n + 1 -1)(n+1-2)(n+1-3)!}{3!(n-2)!})
(frac{(n + 1)(n)(n-1)(n-2)!}{3!(n-2)!})
(frac{(n + 1)(n)(n-1)}{3!})
Since n = 15
(frac{(15 + 1)(15)(15-1)}{3!})
(frac{16 times 15 times 14}{3 times 2 times 1})
= 560

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