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WAEC Further Mathematics 2016 Paper

Question : 13

Total: 40

Simplify

rac{^{n}P_{5}}{^{n}C_{5}}

Solution:

Concept:

Permutation and combination formulas express arrangements and selections, and their ratio simplifies neatly via factorials.

Explanation:

Write the permutation and combination formulas.

{}^{n}P_{5} = \frac{n!}{(n-5)!}

{}^{n}C_{5} = \frac{n!}{(n-5)!5!}

Divide the two expressions.

\frac{{}^{n}P_{5}}{{}^{n}C_{5}} = \frac{\frac{n!}{(n-5)!}}{\frac{n!}{(n-5)!5!}}

Multiply by the reciprocal of the denominator.

= \frac{n!}{(n-5)!} \times \frac{(n-5)!5!}{n!}

Cancel the common terms

n!

and

(n-5)!

= 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120

Answer:

D. 120

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