- #1
ych22
- 115
- 1
Homework Statement
In how many ways can 12 balls be arranged into 4 different rows with each row having at least one ball if there are 6 identical red balls and 6 identical white balls?
Homework Equations
number of combinations of N objects into r groups is [tex]\frac{(N+r-1)!}{N!(r-1)!}[/tex].
The Attempt at a Solution
I thought of two directions
1) First number of arrangements the 12 balls into 4 rows without the requirement of minimum of one ball in each row. Then find the number of combinations in which the requirement is not met. Deduct the latter from the former.
2) Pick the first ball in each row first. Then find the number of combinations to distribute the remaining balls.
Either way, I'm stuck on the math! I think I'm missing a deceptively easy way to look at the problem. Any hints would be appreciated.