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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
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Correct Answer: Option A
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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