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Number of ways in which 6 distinct objec...

Number of ways in which `6` distinct objects can be kept into two identical boxes so that no box remains empty is

A

`31`

B

`32`

C

`63`

D

`64`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` Initially consider the boxes `B_(1)` and `B_(2)` to be distinct.
Object `'a'` can be kept in either of the boxes in `2` ways, similarly for all other things `implies` Total ways `=2^(6)`
But this includes when all the things are in `B_(1)` or `B_(2)`
`implies` Number of ways `=2^(6)-2`
Since the boxes are identical, therefore,
`(2^(6)-2)/(2)=2^(5)-1=31`
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