There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed.Find (d) In how many ways a particular lecturer is excluded

Question

$\begin{array}{1 1}(A)\;10C_2\times 19C_3\\(B)\;12C_2\times 18C_3\\(C)\;8C_2\times 18C_3\\(D)\;\text{None of these}\end{array}$