Test Index

WAEC Further Mathematics 2025 Paper

Question : 18

Total: 40

Simplify

\frac{^n P_4}{ ^n C_4}

Solution:

Concept:

The ratio of a permutation to a combination with the same index reduces to a simple factorial.

Explanation:

Write each expression in factorial form.

^n P_4 = \frac{n!}{(n-4)!}

and

^n C_4 = \frac{n!}{4!(n-4)!}

Now divide:

\frac{^n P_4}{^n C_4} = \frac{\frac{n!}{(n-4)!}}{\frac{n!}{4!(n-4)!}}

Multiply by the reciprocal of the denominator:

\frac{n!}{(n-4)!} \times \frac{4!(n-4)!}{n!}

Cancel

n!

and

(n-4)!

from numerator and denominator.

Only

4!

remains, so the value is

4 \times 3 \times 2 \times 1 = 24

Answer:

24

(Option D).

Go to Question:

Prev Question

Next Question