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 allowing repetition of letters, we can follow these steps:

### Step 1: Identify the letters
The letters in the word "ROSE" are R, O, S, and E. There are a total of 4 distinct letters.

### Step 2: Determine the positions
We need to form a 4-letter word. Since we have exactly 4 letters and we need to use all of them, we will fill all 4 positions in the word.

### Step 3: Calculate the number of choices for each position
- **First position:** We can choose any of the 4 letters (R, O, S, E). So, there are 4 choices.
- **Second position:** After filling the first position, we have 3 letters left. So, there are 3 choices.
- **Third position:** After filling the first two positions, we have 2 letters left. So, there are 2 choices.
- **Fourth position:** After filling the first three positions, we have 1 letter left. So, there is 1 choice.

### Step 4: Multiply the number of choices
To find the total number of 4-letter words, we multiply the number of choices for each position:
\[ \text{Total number of words} = 4 \times 3 \times 2 \times 1 \]

### Step 5: Calculate the result
Calculating the above expression gives:
\[ 4 \times 3 = 12 \\ 12 \times 2 = 24 \\ 24 \times 1 = 24 \]

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

### Final Answer
The number of 4-letter words that can be formed is **24**.

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