Find the number of 4 letter words, with or without meaning, which can be formed out of the letters of the word ROSE, where the repetition of the letters is not allowed.

Options

A. 6
B. 24
C. 120
D. 256

Explanation

To find the number of 4-letter words that can be formed from the letters of the word "ROSE" without repeating any letters, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the letters**: The letters in the word "ROSE" are R, O, S, and E. This gives us a total of 4 unique letters.

2. **Determine the positions**: We need to form a 4-letter word. Since we have 4 letters and we need to fill all 4 positions, we will use all the letters.

3. **Choose letters for each position**:
- For the **first position**, we can choose any of the 4 letters (R, O, S, E). So, there are **4 choices**.
- For the **second position**, since we cannot repeat the letter used in the first position, we have 3 remaining letters to choose from. Thus, there are **3 choices**.
- For the **third position**, we will have 2 letters left after choosing letters for the first two positions. Therefore, there are **2 choices**.
- For the **fourth position**, only 1 letter will be left, so there is **1 choice**.

4. **Calculate the total number of arrangements**: The total number of arrangements can be calculated by multiplying the number of choices for each position:
\[ \text{Total arrangements} = 4 \times 3 \times 2 \times 1 = 24 \]

5. **Conclusion**: Thus, the total number of 4-letter words that can be formed from the letters of the word "ROSE" without repeating any letters is **24**.