In how many ways can the letters of the following words be arranged:
FOREIGN?

Answer

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

### Step 1: Identify the total number of letters
The word "FOREIGN" consists of 7 letters: F, O, R, E, I, G, N.

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

### Step 3: Use the formula for permutations
Since there are no repeating letters, the number of ways to arrange the letters is given by the factorial of the total number of letters. The formula for the number of arrangements (permutations) of n distinct objects is n!.

### Step 4: Calculate the factorial
Here, n = 7 (the number of letters in "FOREIGN"). Therefore, we need to calculate 7! (7 factorial).

\[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]

### Step 5: Perform the multiplication
Calculating this step-by-step:

- 7 × 6 = 42
- 42 × 5 = 210
- 210 × 4 = 840
- 840 × 3 = 2520
- 2520 × 2 = 5040
- 5040 × 1 = 5040

Thus, 7! = 5040.

### Conclusion
The total number of ways to arrange the letters of the word "FOREIGN" is **5040**.

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