Question

Number different ways in which 8 different books can be distributed among 3 student, if each student receives atleast 2 books is _______.

Answer 1

$\left(1\right)$ $\left(2\right)$ $\left(3\right)$

$2$ $2$ $4$ $\Rightarrow {(}^8{C}_2\cdot {}^6{C}_2\cdot {}^4{C}_4)\times 3$

$\left(2\right)$ $3$ $3$ $\Rightarrow {(}^8{C}_2\cdot {}^6{C}_3\cdot {}^3{C}_3{)}^3$

Above combinations can be arranged by $3$ types.

$\therefore$ multiplied by $3$

$\therefore$ Total ways $=\frac{8\times 7}{2\times 1}\times \frac{6\times 5}{2\times 1}\times 1\times 3+\frac{8\times 7}{2\times 1}\times \frac{6\times 5\times 4}{3\times 2\times 1}\times 1\times 3$

$=1260+1680=2940$.