Study the following information carefully to answer the questions that follows
A committee of few members to be formed out of 7 males and 5 females
If the committee of 3 members having atleast 1 female

Options

A. 105
B. 195
C. 240
D. 185

Answer

To solve the problem of forming a committee of 3 members from 7 males and 5 females with the condition that there is at least 1 female, we can break down the solution into several steps.

### Step-by-Step Solution:

1. **Understanding the Conditions**:
We need to form a committee of 3 members that includes at least 1 female. This means we can have the following combinations:
- 1 female and 2 males
- 2 females and 1 male
- 3 females

2. **Calculating Each Case**:
- **Case 1: 1 Female and 2 Males**:
- The number of ways to choose 1 female from 5:
\[ \text{Number of ways} = \binom{5}{1} = 5 \]
- The number of ways to choose 2 males from 7:
\[ \text{Number of ways} = \binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21 \]
- Total ways for this case:
\[ \text{Total} = 5 \times 21 = 105 \]

- **Case 2: 2 Females and 1 Male**:
- The number of ways to choose 2 females from 5:
\[ \text{Number of ways} = \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10 \]
- The number of ways to choose 1 male from 7:
\[ \text{Number of ways} = \binom{7}{1} = 7 \]
- Total ways for this case:
\[ \text{Total} = 10 \times 7 = 70 \]

- **Case 3: 3 Females**:
- The number of ways to choose 3 females from 5:
\[ \text{Number of ways} = \binom{5}{3} = \frac{5 \times 4 \times 3}{3 \times 2 \times 1} = 10 \]

3. **Adding All Cases Together**:
Now, we add the total number of ways from all cases:
\[ \text{Total ways} = 105 + 70 + 10 = 185 \]

### Final Answer:
The total number of ways to form a committee of 3 members with at least 1 female is **185**.