Subjects combinatorics

Gum Ball Combinations

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1. **Stating the problem:** We want to find the possible combinations of gum balls, candies, and toffees in a container such that there is exactly 1 gum ball in the first container, and the total can be either 2 gum balls or 1 gum ball and 1 candy or toffee. 2. **Analyzing the conditions:** - The first container must have exactly 1 gum ball. - The total can be either: - 2 gum balls, or - 1 gum ball and 1 candy, or - 1 gum ball and 1 toffee. 3. **Possible combinations:** - Since the first container has 1 gum ball, the second container can have: - 1 gum ball (making total 2 gum balls), or - 1 candy, or - 1 toffee. 4. **Summary:** The possible pairs are: - (1 gum ball, 1 gum ball) - (1 gum ball, 1 candy) - (1 gum ball, 1 toffee) This satisfies the problem's conditions.