Question 47

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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