In how many different ways can the letters of the word HOME be arranged?

Answer

To find the number of different ways the letters of the word "HOME" can be arranged, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of letters**:
The word "HOME" consists of 4 letters: H, O, M, and E.

2. **Check for repetitions**:
In the word "HOME", all the letters are unique (no letter is repeated).

3. **Use the formula for permutations**:
The number of ways to arrange 'n' distinct objects is given by the formula \( n! \) (n factorial). Since we have 4 distinct letters, we will use \( 4! \).

4. **Calculate \( 4! \)**:
- \( 4! = 4 \times 3 \times 2 \times 1 \)
- Calculate step by step:
- \( 4 \times 3 = 12 \)
- \( 12 \times 2 = 24 \)
- \( 24 \times 1 = 24 \)

5. **Conclusion**:
Therefore, the total number of different ways to arrange the letters of the word "HOME" is **24**.

### Final Answer:
The letters of the word "HOME" can be arranged in **24 different ways**.