If \(\frac{^{8}P_{x}}{^{8}C_{x}} = 6\), find the value of x.
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Correct Answer: Option C
Explanation:
\(\frac{^{8}P_{x}}{^{8}C_{x}} = \frac{8!}{(8 - x)!} ÷ \frac{8!}{(8 - x)! x!} = 6\)
\(\frac{8!}{(8 - x)!} \times \frac{(8 - x)! x!}{8!} = x! = 6\)
\(x = 3\)
\(\frac{^{8}P_{x}}{^{8}C_{x}} = \frac{8!}{(8 - x)!} ÷ \frac{8!}{(8 - x)! x!} = 6\)
\(\frac{8!}{(8 - x)!} \times \frac{(8 - x)! x!}{8!} = x! = 6\)
\(x = 3\)