1. **Problem statement:** We have a box with 5 red, 4 blue, and 3 white balls. We want to find the number of ways to select 3 balls such that each ball is a different color. 2. **Understanding the problem:** Since we want 3 balls all of different colors, we must select exactly one red, one blue, and one white ball. 3. **Formula used:** The number of ways to select one ball from a group of $n$ balls is $\binom{n}{1} = n$. 4. **Calculate each selection:** - Number of ways to select 1 red ball: $\binom{5}{1} = 5$ - Number of ways to select 1 blue ball: $\binom{4}{1} = 4$ - Number of ways to select 1 white ball: $\binom{3}{1} = 3$ 5. **Combine selections:** Since these choices are independent, multiply the number of ways: $$5 \times 4 \times 3 = 60$$ 6. **Final answer:** There are $60$ ways to select 3 balls such that each is a different color.