Question

There are 7 Men and 6 Women. In how many ways can we select 5 members in which at least 3 men should be there:

• A. (A) 836
• B. (B) 256
• C. (C) 495
• D. (D) 756

Answer 1

Answer: (D)

(D) 756

Answer 2

Explanation:
There will be 3 cases for calculating the number of ways to form a committee is as follows,Case 1:3 Men, 2 WomenFor selecting 3 men out of 7 and 2 women out of 6 to form the 5 people committee, we can use the formulas given in the hint as follows,=7C3×6C2=35×15=525Case 2:4 Men, 1 WomanFor selecting 4 men out of 7 and 1 woman out of 6 to form thee 5 people committee, we can use the formulas given in the hint as follows=7C4×6C1=35×6=210Case 3:5 Men, 0 WomenFor selecting 5 men out of 7 and 0 women out of 6 to form thee 5 people committee, we can use the formulas given in the hint as follows,=7C5×6C0=21×1=21Total =525+210+21=756Hence, the correct option is (D).