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# 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

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

Total no of professor =10
Total no of lecturer =20
No of ways a particular lecturer is excluded =$10C_2\times 19C_3$
Hence (D) is the correct answer.