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

Options

A. 520
B. 120
C. 5040
D. none of these

Explanation

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

### Step-by-Step Solution:

1. **Identify the Total Number of Letters**:
The word "SIMPLE" consists of 6 letters: S, I, M, P, L, E.

2. **Check for Repetition**:
In the word "SIMPLE", all letters are unique. There are no repeated letters.

3. **Use the Factorial Formula**:
The number of arrangements of n distinct objects is given by n!. Since we have 6 distinct letters, we will calculate 6!.

4. **Calculate 6!**:
- 6! = 6 × 5 × 4 × 3 × 2 × 1
- Calculate step by step:
- 6 × 5 = 30
- 30 × 4 = 120
- 120 × 3 = 360
- 360 × 2 = 720
- 720 × 1 = 720

5. **Conclusion**:
Therefore, the total number of different ways to arrange the letters of the word "SIMPLE" is 720.

### Final Answer:
The letters of the word "SIMPLE" can be arranged in **720 different ways**.

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