jmc

There are 55 ways to choose the first Republican, 54 ways to choose the second Republican, and 53 ways to choose the third Republican; however, we must divide by $3!$ because order does not matter. So the number of ways to choose Republicans is $\frac{55\times 54\times 53}{3!}=26,235$. There are 45 ways to choose the first Democrat and 44 ways to choose the second Democrat, but we must divide by $2!$ because order does not matter. So the number of ways to choose the Democrats is $\frac{45\times 44}{2!}=990$. So there are $26,235\times 990=\boxed{25,972,650}$ ways to choose a committee.