Test Index

WAEC Further Mathematics 2019 Paper

Question : 5

Total: 39

{}^nC_2

= 15, find the value of n

Solution:

Concept:

This question tests the formula for combinations, i.e. selecting

2

items from

n

items.

Explanation:

The combination formula is

{}^{n}C_{r} = \frac{n!}{r!(n-r)!}

Here

r = 2

, so

{}^{n}C_{2} = \frac{n!}{2!(n-2)!}

Simplify the factorial:

\frac{n!}{(n-2)!} = n(n-1)

Therefore,

{}^{n}C_{2} = \frac{n(n-1)}{2}

It is given that

{}^{n}C_{2} = 15

So,

\frac{n(n-1)}{2} = 15

Multiply both sides by

2

n(n-1) = 30

This gives

n^{2} - n - 30 = 0

Factorise:

(n - 6)(n + 5) = 0

Hence,

n = 6

n = -5

Since

n

must be a positive integer,

n = 6

Answer:

n = 6

, so the correct option is C. 6.

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