In a class there are 10 boys and 8 girls. The teacher wants to select either a boy or a girl to represent the class in a function. The number of ways the teacher can make this selection.

Options

A. 18
B. 80
C. `10^(8)`
D. `8^(10)`

Explanation

To solve the problem of selecting either a boy or a girl from a class of 10 boys and 8 girls, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Students**:
- There are 10 boys and 8 girls in the class.
- Total number of students = Number of boys + Number of girls = 10 + 8 = 18.

2. **Understand the Selection Requirement**:
- The teacher wants to select either one boy or one girl to represent the class.
- This means we need to select 1 student from the total of 18 students.

3. **Use the Combination Formula**:
- The number of ways to select r items from n items is given by the combination formula:
\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
- In our case, we want to select 1 student (r = 1) from 18 students (n = 18).

4. **Calculate the Combination**:
- Substitute n = 18 and r = 1 into the combination formula:
\[ \binom{18}{1} = \frac{18!}{1!(18-1)!} = \frac{18!}{1! \cdot 17!} \]
- Simplifying this, we find:
\[ \binom{18}{1} = \frac{18 \times 17!}{1 \times 17!} = 18 \]

5. **Conclusion**:
- Therefore, the total number of ways the teacher can select either a boy or a girl to represent the class is **18**.