`7!-5!` is equal to :

Options

A. `3!`
B. `4!`
C. `5!`
D. `41xx120`

Answer

To solve the expression \(7! - 5!\), we will first calculate the factorials of 7 and 5.

### Step 1: Calculate \(7!\)
The factorial of 7, denoted as \(7!\), is calculated as follows:
\[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]
Calculating this step-by-step:
- \(7 \times 6 = 42\)
- \(42 \times 5 = 210\)
- \(210 \times 4 = 840\)
- \(840 \times 3 = 2520\)
- \(2520 \times 2 = 5040\)
- \(5040 \times 1 = 5040\)

Thus, \(7! = 5040\).

### Step 2: Calculate \(5!\)
Next, we calculate \(5!\):
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 \]
Calculating this step-by-step:
- \(5 \times 4 = 20\)
- \(20 \times 3 = 60\)
- \(60 \times 2 = 120\)
- \(120 \times 1 = 120\)

Thus, \(5! = 120\).

### Step 3: Subtract \(5!\) from \(7!\)
Now we subtract \(5!\) from \(7!\):
\[ 7! - 5! = 5040 - 120 \]
Calculating this gives:
\[ 5040 - 120 = 4920 \]

### Final Answer
Thus, the value of \(7! - 5!\) is \(4920\).