Suppose you have an odd number of white balls and the same number of blacks balls. 

> 
> How many different ways are there of putting the balls into bins so
>  that you have an odd number of each color in each bin?
> 
> 
> 

For example, if you have $3$ white and $3$ black there are $2$ different ways. You either put them all in one bin or one white and one black in each of $3$ bins. For $5$ white and $5$ white balls there are $4$ different ways. These are:

```
(wwwwwbbbbb)
(wwwbbb)(wb)(wb)
(wwwb)(wbbb)(wb)
(wb)(wb)(wb)(wb)(wb)

```