The number of integers greater than `6,000` that can be formed, using the digits `3, 5, 6, 7 and 8,` without repetition, is :

Explanation

To solve the problem of finding the number of integers greater than 6000 that can be formed using the digits 3, 5, 6, 7, and 8 without repetition, we can break it down into two parts: counting the 4-digit numbers and the 5-digit numbers.

### Step 1: Count the 4-digit numbers greater than 6000

1. **Identify the first digit**: Since the number must be greater than 6000, the first digit can only be 6, 7, or 8.
- Possible choices for the first digit: {6, 7, 8} → 3 options.

2. **Choose the remaining digits**: After choosing the first digit, we have 4 remaining digits to choose from (since we cannot repeat digits).
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