In a class there are 30 boys and 18 girls. The teacher wants to select one boy and one girls. The teacher wants to select one boy and one girls to represent the class for a quliz competition. In how many ways can the teacher make this selection ?

Answer

To solve the problem of selecting one boy and one girl from a class of 30 boys and 18 girls, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Boys and Girls**:
- There are 30 boys and 18 girls in the class.

2. **Selecting One Boy**:
- The number of ways to select one boy from 30 boys can be represented as \( \binom{30}{1} \).
- According to the combination formula, \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \). For \( r = 1 \), this simplifies to \( n \).
- Therefore, \( \binom{30}{1} = 30 \).

3. **Selecting One Girl**:
- Similarly, the number of ways to select one girl from 18 girls is \( \binom{18}{1} \).
- Using the same reasoning as before, \( \binom{18}{1} = 18 \).

4. **Calculating Total Combinations**:
- Since the selection of a boy and a girl are independent events, we multiply the number of ways to select a boy by the number of ways to select a girl.
- Thus, the total number of ways to select one boy and one girl is:
\[ \text{Total Ways} = \binom{30}{1} \times \binom{18}{1} = 30 \times 18 \]

5. **Final Calculation**:
- Now, we compute \( 30 \times 18 \):
\[ 30 \times 18 = 540 \]

### Final Answer:
The teacher can make the selection in **540 ways**.

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