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 ...
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