Question

$12$ different toys are to be distributed to three children equally. In how many ways this can be done$?$

Answer 1

The 12 different toys are to be equally distributed among three children,so each children will get $\frac{12}{3}=4$ toys

$4$ toys can be distributed among $3$ people in:-

$1^{st}$ child will get $4$ toys from $12$ toys in ${}^{12}{C}_4$ ways. Now 8 are remaining.

$2^{nd}$ child will get $4$ toys from $8$ toys in ${}^8{C}_4$ ways.

$3^{rd}$ child will get $4$ toys from $4$ toys in only 1 way.

As above 4 events are occuring simultaneously .So they are to be multiplied with each other

${}^{12}{C}_4\times {}^8{C}_4\times 1$

=$\frac{12!}{8!\times 4!}\times \frac{8!}{4!4!}\times 1=34650$