Simplify \(\frac{^{n}P_{5}}{^{n}C_{5}}\).
FURTHER MATHEMATICS
WAEC 2016
Simplify \(\frac{^{n}P_{5}}{^{n}C_{5}}\).
- A. 80
- B. 90
- C. 110
- D. 120
Correct Answer: D. 120
Explanation
\(\frac{^{n}P_{5}}{^{n}C_{5}} = \frac{n!}{(n-5)!} ÷ \frac{n!}{(n-5)!5!}\)
= \(\frac{n!}{(n-5)!} \times \frac{(n-5)!5!}{n!} = 5! = 120\)
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