Could someone help me with this (possibly simple) problem?....

There are $\displaystyle 2m$ distinct balls. $\displaystyle r$ of them are colored red, $\displaystyle b$ are blue, and the rest are white. How many pairings of the $\displaystyle 2m$ balls can you form such that they do not contain any {red,blue} pair? I know that if $\displaystyle r=b=0$, the answer is $\displaystyle (2m-1)!!$.

Thanks.