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.