In how many other ways can the letters of the word ' SIMPLETON ' be arranged?

Answer

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

### Step 1: Identify the total number of letters
The word "SIMPLETON" consists of 9 letters.

### Step 2: Check for repeated letters
In the word "SIMPLETON", all letters are unique. Therefore, there are no repeated letters.

### Step 3: Use the permutation formula
Since all letters are unique, the number of arrangements (permutations) of the letters can be calculated using the formula for permutations of n distinct objects, which is given by:
\[ n! \]
where \( n \) is the total number of letters.

### Step 4: Calculate the factorial
For "SIMPLETON", we have:
\[ n = 9 \]
Thus, we need to calculate \( 9! \):
\[ 9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]
Calculating this step-by-step:
- \( 9 \times 8 = 72 \)
- \( 72 \times 7 = 504 \)
- \( 504 \times 6 = 3024 \)
- \( 3024 \times 5 = 15120 \)
- \( 15120 \times 4 = 60480 \)
- \( 60480 \times 3 = 181440 \)
- \( 181440 \times 2 = 362880 \)
- \( 362880 \times 1 = 362880 \)

Thus, \( 9! = 362880 \).

### Step 5: Conclusion
The total number of ways to arrange the letters of the word "SIMPLETON" is \( 362880 \).

### Final Answer
The number of ways the letters of the word "SIMPLETON" can be arranged is **362880**.

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