How many numbers are there between 100 and 1000 in which all the digits are distinct?

Explanation

To solve the problem of finding how many numbers between 100 and 1000 have all distinct digits, we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the Range**:
- We are looking for 3-digit numbers between 100 and 999 (since 1000 is not included).

2. **Determine the First Digit**:
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