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JAMB Mathematics 2012 Paper

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Question : 36

Total: 48

Evaluate ⁿ⁺¹C_n-2 If n =15

3630
3360
1120
560

Solution:

Concept:

Use the combination formula:

{}^{n+1}C_{n-2} = \binom{n+1}{n-2}

.

Explanation:

Substitute

n = 15

into the expression.

This gives

{}^{16}C_{13}

.

By the symmetry of combinations,

{}^{16}C_{13} = {}^{16}C_3

.

Now apply the formula:

{}^{16}C_3 = \frac{16!}{3!(16-3)!}

.

So,

{}^{16}C_3 = \frac{16 \times 15 \times 14}{3 \times 2 \times 1}

.

Simplify the numerator:

16 \times 15 \times 14 = 3360

.

Divide by

6

:

\frac{3360}{6} = 560

.

Answer:

D.

560

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