How many 4-letter words can be formed using a,b,c,d and e
(i) without repetiton.
(ii) with repetition.

Answer

To solve the problem of how many 4-letter words can be formed using the letters a, b, c, d, and e, we will consider two cases: (i) without repetition and (ii) with repetition.

### Part (i): Without Repetition

1. **Identify the total number of letters available**: We have 5 letters (a, b, c, d, e).

2. **Determine the number of choices for each letter in the 4-letter word**:
- For the **1st letter**, we can choose any of the 5 letters. So, we have **5 choices**.
- For the **2nd letter**, since we cannot repeat the letter chosen for the 1st position, we have **4 choices** left.
- For the **3rd letter**, we cannot use the letters chosen for the 1st and 2nd positions, leaving us with **3 choices**.
- For the **4th letter**, we cannot use the letters chosen for the 1st, 2nd, and 3rd positions, leaving us with **2 choices**.

3. **Calculate the total number of combinations**:
\[ \text{Total combinations} = 5 \times 4 \times 3 \times 2 \]
\[ = 120 \]

### Part (ii): With Repetition

1. **Identify the total number of letters available**: We still have 5 letters (a, b, c, d, e).

2. **Determine the number of choices for each letter in the 4-letter word**:
- For the **1st letter**, we can choose any of the 5 letters. So, we have **5 choices**.
- For the **2nd letter**, since repetition is allowed, we can again choose any of the 5 letters, giving us **5 choices**.
- For the **3rd letter**, we can again choose any of the 5 letters, giving us **5 choices**.
- For the **4th letter**, we can again choose any of the 5 letters, giving us **5 choices**.

3. **Calculate the total number of combinations**:
\[ \text{Total combinations} = 5 \times 5 \times 5 \times 5 \]
\[ = 5^4 = 625 \]

### Final Answers:
- (i) Without repetition: **120**
- (ii) With repetition: **625**