Five balls are to be placed in three boxes.Each box can hold all five balls.In how many ways can we do this so that no box is empty if

1.balls and boxes are different

2.balls are different but boxes are identical

3.balls are identical but boxes are different

4.balls as well as boxes are different

1. Firstly, where the distribution will be (3,1,1) that is, one box gets three balls and the remaining two boxes get one ball each.

• • No. of ways to choose the box which gets 3 balls = 3 (since, 3 boxes are there).
  • No. of ways to select 3 balls out of 5 is = 5C3.
  • No. of ways to distribute rest of the balls =2.
  • Total no. of ways =60

2. Secondly, where the distribution will be (1,2,2) that is, one box gets one ball and the remaining two boxes get two balls each.

• No. of ways to select 1 balls out of 5 is = 5C1.
• No. of ways to choose the box which gets 1 balls = 3 (since, 3 boxes are there).
• No. of ways to select 2 balls out of remaining 4 to go in second box is = 4C2.
• Total no. of ways = 90

Total:60+90=150.

similarily you can do the rest parts.

in case f any difficulty please feel free to ask