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:
Explanation:
Selecting 3 males from 8 and 4 females from 7 can be done in 8C3 × 7C4 = 56 × 35 = 1960
Raj and Rani together cannot be in the committee.
Selection of both Raj and Rani can happen in 7C2 × 6C3 = 21 × 20 = 420
Required number of ways = 1960 – 420 = 1540
Hence, option (c).
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