`n` different toys have to be distributed among `n` children. Find the number of ways in which these toys can be distributed so that exactly one child gets no toy.

Explanation

There are `n ` ways to choose the child that will not get any toy.


There are `C(n,2)` ways to choose `2` toys for a child that will have two toys.

There are `n-1` ways to choose the child, who will get the `2` toys.

There are `(n-2)!` ways to distribute the rest `n-2` toys to the rest `n-2` children.

`:.` Total number of ways ` = n*C(n,2)*(n-1)*(n-2)! = n!C(n,2)`.