Question 118

# In an Engineering College in Pune, 8 males and 7 females have appeared for Student Cultural Committee selection process. 3 males and 4 females are to be selected. The total number of ways in which the committee can be formed, given that Mr. Raj is not to be included in the committee if Ms. Rani is selected, is:

Solution

Mr. Raj is not to be included in the committee if Ms. Rani i.e. they both cannot be included together.
Let
i) Raj is selected and Rani is not.
Thus, the remaining 2 males can be selected $$^7C_{2}$$ ways and the remaining 4 females can be selected in $$^6C_{4}$$ ways.
Thus, the total number of ways = $$^7C_{2}$$*$$^6C_{4}$$ = $$315$$
ii) Raj is not selected and Rani is selected.

Thus, the remaining 3 males can be selected $$^6C_{3}$$ ways and the remaining 3 females can be selected in $$^6C_{3}$$ ways

Thus, the total number of ways = $$^7C_{3}$$*$$^6C_{3}$$ = $$700$$
iii) Both are not selected.

Thus, the remaining 3 males can be selected $$^7C_{3}$$ ways and the remaining 4 females can be selected in $$^6C_{4}$$ ways.
Thus, the total number of ways = $$^7C_{3}$$*$$^6C_{4}$$ = $$525$$
Thus, the total number of ways = $$315+700+525 = 1540$$
Hence, option C is the correct answer.