Question

In how many ways can 9 different books be divided among three boys A, B and C so that they receive 4, 3 and 2 books respectively?

Answer 1

At first, we need to select 4 books for boy A.

4 books can be selected in $C(9,4)$ ways.

Now we have 5 books and we need to select 3 books for boy B.

3 books can be selected in $C(5,3)$ ways.

So, we have only 2 books and there is only 1($=C(2,2))$ way to select 2 books for boy C.

Number of ways =$C(9,4)\times C(5,3)\times C(2,2)=126\times 10\times 1=1260$ .

Answer: 1260.