Find the number of ways of selections of 3 balls out of 9 red distinct balls and 6 balck distnct balls if at least one balck ball is here in each selection.

Explanation

To solve the problem of finding the number of ways to select 3 balls from 9 distinct red balls and 6 distinct black balls with the condition that at least one black ball must be included in each selection, we can break it down into cases based on the number of black balls selected.

### Step-by-Step Solution:

1. **Identify Cases**: We need to consider three cases based on the number of black balls selected:
- Case 1: 1 black ball and 2 red balls
- Case 2: 2 black balls and 1 red ball
- Case 3: 3 black balls
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