Question: Number of ways in which 5 different toys can be distributed among 5 children if exactly one child do...

Question

Number of ways in which 5 different toys can be distributed among 5 children if exactly one child do not get any toy

Answer 1

Solution

\ 5 toys has to be distributed among 4 children after one of them is excluded. Which means one of them will get 2 toys.

So this can be done is

= $\frac{5C_{2}.^{3}C_{1} \times^{2}C_{1} \times^{1}C_{1} \times 4!}{3!}$ $\left\lbrack \begin{aligned} & asgroup \\ & willbe2,1,1,1 \end{aligned} \right\rbrack$

= 10 × 3 × 2 × 4 = 240

Now one child can be rejected is $5C_{1}$ = 5 ways

\ Total ways = 5 × 240 = 1200