Subjects combinatorics

Meal Combinations 1E8613

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1. **State the problem:** A restaurant menu has 3 sandwiches, 4 drinks, and 5 desserts. We want to find how many unique meals are possible if a meal consists of one item from each category. 2. **Formula used:** The total number of unique meals is the product of the number of choices in each category because each choice is independent. So, total meals = number of sandwiches \( \times \) number of drinks \( \times \) number of desserts. 3. **Calculate initial total:** $$3 \times 4 \times 5 = 60$$ So, there are 60 unique meals initially. 4. **If 2 more desserts are added:** The number of desserts becomes \(5 + 2 = 7\). 5. **Calculate new total:** $$3 \times 4 \times 7 = 84$$ 6. **Conclusion:** Adding 2 more desserts increases the total number of unique meals from 60 to 84.