If `n! - n = n`, then the value of n is :

Options

A. 4
B. 5
C. 6
D. 3

Explanation

To solve the equation \( n! - n = n \), we can simplify it step by step.

### Step 1: Rewrite the equation
We start with the equation:
\[ n! - n = n \]
We can rearrange it to:
\[ n! = n + n \]
This simplifies to:
\[ n! = 2n \]

### Step 2: Test the values of \( n \)
We will test the given options one by one to find the value of \( n \).

#### Option 1: \( n = 4 \)
Calculate \( 4! \):
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]
Now check if \( 4! = 2 \times 4 \):
\[ 24 \neq 8 \quad \text{(Not a solution)} \]

#### Option 2: \( n = 5 \)
Calculate \( 5! \):
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]
Now check if \( 5! = 2 \times 5 \):
\[ 120 \neq 10 \quad \text{(Not a solution)} \]

#### Option 3: \( n = 6 \)
Calculate \( 6! \):
\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \]
Now check if \( 6! = 2 \times 6 \):
\[ 720 \neq 12 \quad \text{(Not a solution)} \]

#### Option 4: \( n = 3 \)
Calculate \( 3! \):
\[ 3! = 3 \times 2 \times 1 = 6 \]
Now check if \( 3! = 2 \times 3 \):
\[ 6 = 6 \quad \text{(This is a solution)} \]

### Conclusion
The value of \( n \) that satisfies the equation \( n! - n = n \) is:
\[ \boxed{3} \]