1. **Problem statement:** Helen wants to choose one main course and one dessert from 6 main courses and 8 desserts. 2. **Formula for combinations:** When choosing one item from each of two categories, the total number of combinations is the product of the number of choices in each category. 3. **Explanation:** Since Helen must pick one main course and one dessert, multiply the number of main courses by the number of desserts. 4. **Intermediate work:** Total combinations = $6 \times 8$ 5. **Problem statement:** In a rugby tournament with 10 teams, each team plays every other team exactly once. 6. **Formula for total games:** The total number of games is the number of unique pairs of teams, which is given by the combination formula $\binom{n}{2} = \frac{n(n-1)}{2}$ where $n$ is the number of teams. 7. **Explanation:** Each game is played between two different teams, so count all unique pairs. 8. **Intermediate work:** Total games = $\frac{10 \times 9}{2}$ This method helps you find the number of combinations and total games without directly giving the final numbers.