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## Homework Statement

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

## Homework Equations

## The Attempt at a Solution

I began by finding the number of ways of distributing 5 balls among 3 people --->

1) Number of ways of selecting 3 balls out of 5 is 10

2) Number of ways of arranging the 3 balls among 3 people is 6.

Hence total number of ways = 60

Now, the remaining 2 balls have to be distributed among 5 people ---->

1) both the balls can be given to one man or can be distributed

2) if both the balls are given to a single man, then total ways = 3

3) if one ball is given to one of the three, then total ways = 6.

Hence total number of ways = 6+3 = 9

So, in my view, the answer should be 60+9 = 69.

But the answer is 150 ... far more than my answer.

I don't want to know a new method because a lot are available on the internet. Please let me know what's wrong with my approach ...

Thanks in advance for any help

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