Jambmaths question:
Evaluate $^{n+1}{{C}_{n-2}}$ if n = 15
Option A:
3630
Option B:
3360
Option C:
1120
Option D:
560
Jamb Maths Solution:
$\begin{align} & ^{15+1}{{C}_{15-2}}{{=}^{16}}{{C}_{13}}=\frac{16!}{13!(16-13)!} \\ & ^{15+1}{{C}_{15-2}}=\frac{16!}{13!3!} \\ & ^{15+1}{{C}_{15-2}}=\frac{16\times 15\times 14\times 13!}{13!\times 3\times 2\times 1} \\ & ^{15+1}{{C}_{15-2}}=\frac{16\times 15\times 14}{3\times 2\times 1} \\ & ^{15+1}{{C}_{15-2}}=16\times 5\times 7 \\ & ^{15+1}{{C}_{15-2}}=560 \end{align}$
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