There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturers is to be formed. In how many ways can a committee be formed?

Question

$\begin{array}{1 1}(A)\;20C_3\times 10C_2\\(B)\;10C_3\times 5C_2\\(C)\;15C_3\times 5C_2\\(D)\;\text{None of these}\end{array}$