How many 3-letter words can be formed using a, b, c, d, e if
(i) repetition of letters is not allowed?
(ii) repetition of letters is allowed?

Explanation

To solve the question of how many 3-letter words can be formed using the letters a, b, c, d, e, we will break it down into two parts:

### Part (i): Repetition of letters is not allowed.

1. **Choose the first letter**: We have 5 options (a, b, c, d, e).
2. **Choose the second letter**: Since repetition is not allowed, we can only choose from the remaining 4 letters.
3. **Choose the third letter**: Again, since repetition is not allowed, we can only choose from the remaining 3 letters.

Now, we can calculate the total number of combinations:
- Total combinations = (Choices for 1st letter) × (Choices for 2nd letter) × (Choices for 3rd letter)
- Total combinations = 5 × 4 × 3

Calculating this gives:
- Total combinations = 60

### Part (ii): Repetition of letters is allowed.

1. **Choose the first letter**: We have 5 options (a, b, c, d, e).
2. **Choose the second letter**: Since repetition is allowed, we still have 5 options.
3. **Choose the third letter**: Again, since repetition is allowed, we have 5 options.

Now, we can calculate the total number of combinations:
- Total combinations = (Choices for 1st letter) × (Choices for 2nd letter) × (Choices for 3rd letter)
- Total combinations = 5 × 5 × 5

Calculating this gives:
- Total combinations = 125

### Final Answers:
- (i) The number of 3-letter words that can be formed without repetition is **60**.
- (ii) The number of 3-letter words that can be formed with repetition is **125**.