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

Options

A. 360
B. 5040
C. 720
D. 780

Answer

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

### Step 1: Count the number of letters in the word
The word 'NUMBER' consists of 6 letters: N, U, M, B, E, R.

### Step 2: Determine if any letters are repeated
In the word 'NUMBER', all letters are unique. There are no repeating letters.

### Step 3: Use the factorial to calculate arrangements
Since there are 6 unique letters, the number of different arrangements can be calculated using the factorial of the number of letters. This is represented as \(6!\) (6 factorial).

### Step 4: Calculate \(6!\)
To calculate \(6!\):
\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]

### Step 5: Perform the multiplication
Calculating step by step:
- \(6 \times 5 = 30\)
- \(30 \times 4 = 120\)
- \(120 \times 3 = 360\)
- \(360 \times 2 = 720\)
- \(720 \times 1 = 720\)

Thus, \(6! = 720\).

### Step 6: Conclusion
The total number of different ways the letters of the word 'NUMBER' can be arranged is **720**.

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