Hi,

Say I have 7 balls I can put in 7 different buckets. Define Xn to be the number of buckets with n balls. For instance X3 = 1 is the number of buckets with one ball in them.
What is the probability that X3 = 3?

My solution is as follows:

Pick first bucket with three balls, pick 2nd bucket with 3 balls, pick remaining bucket. That gives
(7 * (7 choose 3) * 6 * (4 choose 3) * 5) / 7^7

The solution manual says that it should be ((7 choose 2) * (7 choose 3) * (4 choose 3) * 5) / 7^7

It seems that the difference is because I am counting order whereas the solution manual is not. Why does order not matter?