If $^{n} P_{4} :^{n} P_{5} = 1 : 2$ find ' $n$ '

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Solution

$^{n} P_{4} :^{n} P_{5} = 1 : 2 \Rightarrow \frac{\frac{n!}{(n - 4)!}}{\frac{n!}{(n - 5)!}} = \frac{1}{2} \Rightarrow \frac{(n - 5)!}{(n - 4)!} = \frac{1}{2} \Rightarrow (n - 4) = 2 \Rightarrow n = 6$

Hence the correct answer is $6$

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Similar questions

^{n} P_{4} :^{n} P_{5}

=

1 : 2

n

=

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

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

n

(i)^{n} P_{5} = 42^{n} P_{3}, n > 4

(i i) \frac{^{n} P_{4}}{^{n - 1} P_{4}} = \frac{5}{3}, n > 4

^{n} P_{5} :^{n - 1} P_{5} = 3 : 2

n

^{n} p_{4} :^{n - 1} p_{3} = 9 : 1

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