- #1

erisedk

- 374

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## Homework Statement

The total number of ways in which 5 balls of different colors can be distributed among 3 persons so that each person gets at least one ball is

Ans: 150

## Homework Equations

## The Attempt at a Solution

I don't understand what's wrong with my answer.

In case of each person getting one ball and the remaining two balls going to a single person, I have 5*4*3*3 ways. 5*4*3 for the first three balls and then the remaining two balls have three options, therefore the final *3

In case of the remaining two balls going to different people, I have 5*4*3*6 ways to do so, the final*6 because I have 3 spots and I have two pick two balls, and order matters as the balls are different.

Adding 5*4*3*3 + 5*4*3*6, I get 540.

What am I doing wrong?

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