Find the number of groups that can be made from 5 different green balls., 4 different blue balls and 3 different red balls, if at least 1 green and 1 blue ball is to be included.

Explanation

To solve the problem of finding the number of groups that can be made from 5 different green balls, 4 different blue balls, and 3 different red balls with the condition that at least one green and one blue ball must be included, we can follow these steps:

### Step-by-Step Solution:

1. **Choosing Green Balls:**
- We need to select at least one green ball from the 5 available. The number of ways to choose at least one green ball can be calculated as:
\[
\text{Ways to choose green balls} = 5C1 + 5C2 + 5C3 + 5C4 + 5C5
...