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Question

Find the total number of ways in which 30 distinct objects can be put into two different boxes so that no box remains empty.

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Solution

These are 30 objects,, and each object has 2
options i.e, either go in box A or in box 13.

Hence Total ways = 2×2×30 times=230

Now in these 230 ways, these would be one
particular instance when all objects would have gone to box A.
Also, there be one particular instance when all object would have gone to box B.
so these are 2 instance when one of the box would have been empty.

Required number of ways =2302

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