Question

The number of ways $5$ objects be divided among the persons $A$ and $B$ if

• A. no one gets all the objects is $30$
• B. one can get all the object is $30$
• C. one can get all the object is $32$
• D. no one gets all the objects is $31$

Answer 1

Answer: (A), (C)

The correct options are
A no one gets all the objects is $30$
C one can get all the object is $32$

Now each object has only two option either it can be with $A$ or with $B$
So required number of ways $=2^5-2=30$
[$\because A$ and $B$ both gets atleast one object]

If one can get all the objects
Hence required number of ways $=2^5=32$