The number of ways of distributing `3` identical physics books and `3` identical methematics books among three students such that each student gets at least one books is

Options

A. `45`
B. `55`
C. `64`
D. `72`

Answer

B

Explanation

`(b)` `n(A)=^(3+2-1)C_(2-1)xx^(3+2-1)C_(2-1)=16`
`n(B)=n(C )=16`
`n(AnnB)=^(3+2-1)C_(1-1)xx^(3+2-1)C_(1-1)`
`=1=n(BnnC)=n(AnnC)`
`n(AnnBnnC)=0`
Required no. of ways `=100-(16+16+16-1-1-1+0)=55`