IF `1 times 2 times 3 times ………. N` is denoted by `angle n` then `(angle8+angle7-angle7)` is equal to

Options

A. `6 times 8 times angle6`
B. `7 times 8 times angle6`
C. `6 times 7 times angle8`
D. `7 times 8 times angle7`

Answer

To solve the problem, we need to evaluate the expression \( \angle 8 + \angle 7 - \angle 7 \), where \( \angle n \) denotes \( n! \) (n factorial).

### Step-by-step Solution:

1. **Identify the Factorials**:
- We know that \( \angle n = n! \). Therefore:
- \( \angle 8 = 8! \)
- \( \angle 7 = 7! \)

2. **Substitute the Factorials into the Expression**:
- Substitute the factorials into the expression:
\[ \angle 8 + \angle 7 - \angle 7 = 8! + 7! - 7! \]

3. **Simplify the Expression**:
- Notice that \( 7! - 7! = 0 \):
\[ 8! + 7! - 7! = 8! \]

4. **Calculate \( 8! \)**:
- Now, we need to calculate \( 8! \):
\[ 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320 \]

5. **Final Result**:
- Therefore, the value of \( \angle 8 + \angle 7 - \angle 7 \) is:
\[ \boxed{40320} \]