Boys Together
1. **Problem statement:** We need to find the number of ways to seat 6 girls and 2 boys in a row such that the two boys are always seated together.
2. **Understanding the problem:** Treat the two boys as a single unit since they must sit together. This reduces the problem to arranging 7 units: 6 girls + 1 "boy pair".
3. **Formula and rules:**
- Number of ways to arrange $n$ distinct objects in a row is $n!$.
- Since the two boys can switch seats within their pair, multiply by $2!$ for their internal arrangements.
4. **Calculations:**
- Arrange 7 units: $7!$
- Arrange 2 boys within their unit: $2!$
- Total arrangements: $7! \times 2!$
5. **Evaluate:**
- $7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040$
- $2! = 2$
- Total = $5040 \times 2 = 10080$
6. **Answer:** There are **10080** ways to seat 6 girls and 2 boys in a row with the boys together.