Answer to Question #56762 in Combinatorics | Number Theory for samagra

Question

5 balls are to be placed in 3 boxes. Each box can hold all 5 balls. In how many different ways can we place the balls so that no box remains empty if, (i) balls & boxes are different (iii) balls are different but boxes are identical (ii) balls are identical but boxes are different (iv) balls as well as boxes are identical