If 2nP3=100×nP2 find n?(This is a question from permutation)

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Answer 1 · 2018-01-11T11:50:59

$52$ $52$ .

Recall that, $_{n} P_{r} = \frac{n!}{(n - r)!}$ $""_nP_r=(n!)/((n-r)!)$ .

$:. 2""_nP_3=100"_nP_2$ .

$:. 2*(n!)/((n-3)!)=100*(n!)/((n-2)!)$ .

$:. ((n-2)!)/((n-3)!)=100/2=50$ .

$:. [1*2*3*...(n-3)(n-2)]/[1*2*3*...(n-3)]=50$ .

$:. n-2=50$ .

$rArr n=52$ .