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Evaluate ⁿ⁺¹C_n-2 If n =15...

Evaluate ⁿ⁺¹C_n-2 If n =15

A.

3630

B.

3360

C.

1120

D.

560

View answer & explanation

Correct answer is D

$\frac{n + 1 (n - 2)}{(n + 1)!}$

$\frac{(n + 1) + (n - 2)!(n - 2)!}{(n + 1)!}$

$\frac{(n + 1)(n + 1 -1)(n+1-2)(n+1-3)!}{3!(n-2)!}$

$\frac{(n + 1)(n)(n-1)(n-2)!}{3!(n-2)!}$

$\frac{(n + 1)(n)(n-1)}{3!}$

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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