If $^{n} P_{4} :^{n} P_{5}$ $=$ $1 : 2$ , then $n$ $=$

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Solution

The correct option is C 6
From question, we have
$\frac{^{n} P_{4}}{^{n} P_{5}} = \frac{1}{2}$
$\Rightarrow \frac{\frac{n!}{(n - 4)!}}{\frac{n!}{(n - 5)!}} = \frac{1}{2}$
$\Rightarrow \frac{n - 5}{n - 4} = \frac{1}{2}$
$\Rightarrow 2 n - 10 = n - 4$
$\Rightarrow n = 6$

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Similar questions

^{n} P_{4} :^{n} P_{5} = 1 : 2

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(i) If $^{n} P_{4} :^{n} P_{5} = 1 : 2$ find n.

(ii) If $^{n - 1} P_{3} :^{n + 1} = 5 : 12,$ find n.

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