Question

in how many ways 7 different objects can be divided among 3 persons so that either one or two of them do not get any objexts

Answer 1

When one gets all objects:

Total cases = 3

When two gets all objects:

Let us consider A and B gets all the objects. Now 7 objects has to be distributed between two members.

So we choose 1,2,3,....6 objects in ${{7}\choose{1} }+{{7}\choose{2} }+{{7}\choose{3} }+{{7}\choose{4} }+{{7}\choose{5} }+{{7}\choose{6} }=126$ ways.

Now this can be between B and C and C and A.

This total cases=126*3=378

Total cases=378+3=381