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

1 Answer
Jan 11, 2018

# 52#.

Explanation:

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#.