Question

In how many different ways can eight different books be distributed among $31$ students if each receive atleast $2$ books.

Answer 1

(i) ${}^8{C}_2\times {}^6{C}_2\times {}^4{C}_4\times 3!$

(ii) ${}^8{C}_2\times {}^6{C}_3\times {}^3{C}_3\times 3!$

$\therefore$ Total number of ways$=3\times {}^8{C}_2[{}^6{C}_2+{}^6{C}_3]$

$=3\times 28(15+20)$

$=2940$.