Five people will be chosen from a group of seven men and six women to create a committee, with at least three males on the committee. How many different ways can it be done?
A. 564
B. 645
C. 735
D. 756
Answer:D
Five people will be chosen from a group of seven men and six women to create a committee, with at least three males on the committee. How many different ways can it be done?
A. 564 B. 645 C. 735 D. 756
Explanation: We might have 3 men and 2 women, 4 men and 1 woman, or 5 men and 1 woman (5 men only 7 x 6 x 5/3 x 2 x 1 2 x 1 x 6 x 5/2 x1 + (7C3 x 6C1) + (7C3 x 6C2) + (7C4 x 6C1) + (7C5) = 7 x 6 x 5/3 x 2 x 1 2 x 1 x 6 x 5/2 x1 + (7C3 x 6C1) + (7C3 x 6C1) + (7C3 x 6 (7C2)= 525 + 7 x 6 x 5 x 6/3 x 2 x 1 2 x 1 + 7 x 6/2 x 1 = (756 + 525 + 210 + 21).