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

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Answer 1 · 2018-01-11T11:50:59

# 52#.

Recall that, #""_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#.