`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

If exactly one child gets no toy, then exactly one child must get two toys and rest (n-2) gets one toy each.
The division tree is as shown in the following figure.

The number of ways of division in the groups as shown in the figure is `(n!)/(0!2!(1!)^(n-2)(n-2)!)=(n!)/(2!(n-2)!)= .^(n)C_(2)`
The number of ways of distribution of these n groups among n children is n!. Then, the total number of ways of distributions is `. ^(n)C_(2)xxn!`.