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The number of ways of distributing 3 ide...

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

A

`45`

B

`55`

C

`64`

D

`72`

Text Solution

Verified by Experts

The correct Answer is:
B
`(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`
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