In how many ways we can select a six members team from 8 men and 5 women. In which women are dominating?

Options

A. 148
B. 48
C. 60
D. can't determined

Answer

To solve the problem of selecting a six-member team from 8 men and 5 women, where women are dominating, we need to determine the combinations that satisfy the condition of having more women than men in the team.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have a total of 13 individuals (8 men and 5 women). We need to form a team of 6 members such that the number of women is greater than the number of men.

2. **Identifying Valid Combinations**:
The possible distributions of men and women in the team of 6, where women dominate, are:
- 5 women and 1 man
- 4 women and 2 men

We cannot have 3 women and 3 men since that does not satisfy the condition of women dominating.

3. **Calculating Combinations for Each Case**:
- **Case 1: 5 Women and 1 Man**:
- Choose 5 women from 5: \( \binom{5}{5} = 1 \)
- Choose 1 man from 8: \( \binom{8}{1} = 8 \)
- Total combinations for this case: \( 1 \times 8 = 8 \)

- **Case 2: 4 Women and 2 Men**:
- Choose 4 women from 5: \( \binom{5}{4} = 5 \)
- Choose 2 men from 8: \( \binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28 \)
- Total combinations for this case: \( 5 \times 28 = 140 \)

4. **Adding the Combinations**:
Now, we add the total combinations from both cases:
\[ \text{Total combinations} = 8 + 140 = 148 \]

5. **Final Answer**:
Therefore, the total number of ways to select a six-member team from 8 men and 5 women, where women are dominating, is **148**.