If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5. and 7. what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed?

Explanation

To solve the problem, we will break it down into two parts: (i) when the digits can be repeated, and (ii) when the digits cannot be repeated.

### Part (i): Digits are Repeated

1. **Determine the total number of 4-digit numbers greater than 5000:**
- The first digit can be either 5 or 7 (to ensure the number is greater than 5000).
- If the first digit is 5, the remaining three digits can be any of the 5 digits (0, 1, 3, 5, 7).
- If the first digit is 7, the remaining three digits can also be any of the 5 digits.
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