Question

In how many ways can $22$ distinct books be given to $5$ students so that two students have $5$ books each and another three students have $4$ books each?

Answer 1

The 2 students can be selected in ${}^5{C}_2$ ways.

Now, the first 5 books to be given to the first student can be done in ${}^{22}{C}_5$ ways.

Similarily next 5 books can be selected in ${}^{17}{C}_5$ ways.

Now the remaining 12 can be selected in 3 groups of 4 by ${}^{12}{C}_4{\times }^8{C}_4$

Hence, total = ${}^5{C}_2{\times }^{22}{C}_5{\times }^{17}{C}_5{\times }^{12}{C}_4{\times }^8{C}_4$