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  • Number of ways in which 6 distinct objects can be kept into two identical boxes so that no box remains empty is  Option: 1

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

 

Option: 1

31


Option: 2

32


Option: 3

63


Option: 4

64


Answers (1)

best_answer

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 \Rightarrow \text{Total ways } =2^6
But this includes when all the things are in B_1 or B_2        \Rightarrow Number of ways = 2^6-2
Since the boxes are identical, therefore,

\frac{2^6-2}{2}=2^5-1=31

 

Posted by

jitender.kumar

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