How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?

Explanation

To solve the problem of how many 3-digit numbers can be formed from the digits 1, 2, 3, 4, and 5 under two different conditions (with and without repetition), we will break it down step by step.

### Part (i): Repetition of the digits is allowed

1. **Choosing the first digit**: Since repetition is allowed, we can choose any of the 5 digits (1, 2, 3, 4, 5) for the first position.
- **Choices for the first digit**: 5

2. **Choosing the second digit**: Again, since repetition is allowed, we can choose any of the 5 digits for the second position as well.
...