Simplify \(\frac{^{n}P_{4}}{^{n}C_{4}}\)
FURTHER MATHEMATICS
WAEC 2006
Simplify \(\frac{^{n}P_{4}}{^{n}C_{4}}\)
- A. 24
- B. 18
- C. 12
- D. 6
Correct Answer: A. 24
Explanation
\(^{n}P_{4} = \frac{n!}{(n - 4)!}\)
\(^{n}C_{4} = \frac{n!}{(n - 4)! 4!}\)
\(\frac{^{n}P_{4}}{^{n}C_{4}} = \frac{n!}{(n - 4)!} ÷ \frac{n!}{(n - 4)! 4!}\)
= \(4! = 24\)
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