In how many ways can 8 persons stand in the form of a ring ?

Options

A. 8!
B. `7!`
C. `6!`
D. `(7!)/(2)`

Answer

To determine the number of ways in which 8 persons can stand in the form of a ring, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Arrangement in a Ring**:
When arranging objects in a ring, one object can be fixed to eliminate the effect of rotations. This is because rotating the arrangement does not create a new arrangement.

2. **Fixing One Person**:
We can fix one person in one position. This means we only need to arrange the remaining 7 persons around this fixed person.

3. **Calculating the Arrangements**:
The number of ways to arrange the remaining 7 persons is given by the factorial of the number of persons to arrange. Thus, we calculate \(7!\) (7 factorial).

4. **Calculating \(7!\)**:
\(7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040\).

5. **Final Answer**:
Therefore, the total number of ways in which 8 persons can stand in the form of a ring is \(5040\).

### Final Answer:
The number of ways 8 persons can stand in the form of a ring is **5040**.