Question

Seven different objects must be divided among three people. In how many ways can it be done if one or two of them can get no objects?

Answer 1

when one of them do not get any object, then the objects will be divided among $2$ persons.

No. of ways to select $2$ persons =$3C2$

No. of ways to divide $7$ objects among $2$ persons = $2^7$

So required no. of ways= ${(}^3{C}_2\left)\right(2^7-2)=378$[when none of them get any object]
when objects are given to only one person.

Required. no. of ways(two of them don't get any object)=${}^3{C}_1=3.$

So, total no. of ways = $378+3=381$