from a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. in how many ways can it be done?
from a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. in how many ways can it be done?
Answer:
find the number of ways to select 3 men out of 7 and 2 women out of 6 to form a 5 people committee, you can use the formula:
- C(7,3) * C(6,2) = 35 * 15 = 525
Therefore, there are 525 different ways to select 3 men out of 7 and 2 women out of 6 to form a 5 people committee.
- C(7,4) * C(6,1) = 35 * 6 = 210
Therefore, there are 210 different ways to select 4 men out of 7 and 1 woman out of 6 to form a 5 people committee.
For selecting 5 men out of 7 and 0 women out of 6 to form thee 5 people committee
- C(7,5) * C(6,0) = 21 * 1 = 21
Therefore, there are 21 different ways to select 5 men out of 7 and 0 women out of 6 to form a 5 people committee.
Total: 525+210+21=756