How can I select a committee of 5 people out of 10 men and 8 women. Women must be the majority in the committee. One man must be in the committee.
So you must select 3 or 4 women
= C(8,3)*C(10,2) + C(8,4)*C(10,1)
= 56(45) + 70(10)
= 3220
check my arithmetic
To form a committee of 5 people out of 10 men and 8 women, with women being the majority and at least one man must be included, you can follow these steps:
Step 1: Select the required minimum members
- Choose 1 man from the 10 available men. This can be done in C(10,1) ways, which means selecting 1 man out of 10.
- Next, choose 2 more women from the 8 available women. This can be done in C(8,2) ways, which means selecting 2 women out of 8.
Step 2: Select the remaining members to meet the total of 5 members
- Since you have already selected 1 man and 2 women, you need to select 2 more members.
- You can choose these additional members from the remaining pool, which are 9 men (since one man has already been selected) and 6 women (since two women have already been selected).
Step 3: Calculate the total number of ways to form the committee
- Multiply the number of ways from each step to get the total number of committees.
- Total number of committees = C(10,1) * C(8,2) * C(9,2)
Step 4: Calculate the result
- Plug in the values and calculate the final result.
Therefore, to select a committee of 5 people out of 10 men and 8 women, with women being the majority and at least one man included, you can follow these steps and calculate the result.