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

Options

A. 720
B. 120
C. 5040
D. 270

Explanation

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

### Step 1: Count the number of letters in the word
The word "SECOND" consists of 6 letters: S, E, C, O, N, D.

### Step 2: Check for repetitions
In the word "SECOND", all letters are unique. There are no repeating letters.

### Step 3: Use the formula for permutations
Since there are no repeating letters, the number of different arrangements (permutations) of the letters can be calculated using the factorial of the number of letters. The formula for the number of arrangements of n distinct objects is given by n!.

For the word "SECOND", we have:
- n = 6 (since there are 6 letters)

So, we need to calculate 6!.

### Step 4: Calculate 6!
Now we will calculate 6! (6 factorial):
6! = 6 × 5 × 4 × 3 × 2 × 1

Calculating step by step:
- 6 × 5 = 30
- 30 × 4 = 120
- 120 × 3 = 360
- 360 × 2 = 720
- 720 × 1 = 720

Thus, 6! = 720.

### Conclusion
The total number of different ways the letters of the word "SECOND" can be arranged is **720**.

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