Book Maths Puzzle HR Interview Interview

Five balls needs to be placed in three boxes. Each box can hold all the five balls. In how many ways can the balls be placed in the boxes so that no box remains empty If all balls and boxes are identical but the boxes are placed in a row.

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Book Other Question
Eight balls of different colours need to be placed in three boxes of different sizes. Each box can hold all the eight balls. In how many ways can the balls be placed in the boxes so that no box remains empty ? In how many ways can 7 different balls be distributed in 5 different boxes if any box can contain any number of balls, no box can be empty and ball 3 and ball 5 cannot be put in the same box?