Question

From a group of 7 men and 6 women, 5 persons are to be selected so that at least 3 men are on the committee. In how many ways can this be done?

• A. 500
• B. 525
• C. 756
• D. 625
• E. 850

Hint:

"At least" problems require you to sum all possible scenarios that meet or exceed the minimum requirement.

Answer 1

The Correct Option is C

Step 1: Analyse options.
- Case 1 (3 Men, 2 Women): $^7C_3 \times ^6C_2 = 35 \times 15 = 525$. - Case 2 (4 Men, 1 Woman): $^7C_4 \times ^6C_1 = 35 \times 6 = 210$. - Case 3 (5 Men, 0 Women): $^7C_5 \times ^6C_0 = 21 \times 1 = 21$. - Total ways = $525 + 210 + 21 = 756$.
Step 2: Conclusion.
The committee can be formed in 756 ways. Final Answer: (c) 756