Question

In how many ways can $9$ different books be distributed among three students if each receives at least $2$ books.

Answer 1

Possible arrangements so that each student gets at least 2 books are

$2,2,5=$ $\left({{}^{9}C}_2{{}^{9}C}_2{{}^{9}C}_5\right)3!$

$2,3,4=$ $\left({{}^{9}C}_2{{}^{9}C}_3{{}^{9}C}_4\right)3!$

$3,3,3,=$ $\left({{}^{9}C}_3{{}^{9}C}_3{{}^{9}C}_3\right)3!$

Total ways $=22176$