What is the number of ways in which n different objects can be arranges at a round table ?

Answer

To find the number of ways in which \( n \) different objects can be arranged at a round table, we can follow these steps:

### Step 1: Understand the concept of arrangements at a round table
When arranging objects in a straight line, the total number of arrangements of \( n \) different objects is given by \( n! \) (n factorial). However, when arranging these objects in a circle, we need to account for the fact that rotations of the same arrangement are considered identical.

### Step 2: Adjust for circular arrangements
To adjust for the circular arrangement, we fix one object in place and arrange the remaining \( n-1 \) objects around it. This is because rotating the entire arrangement does not create a new arrangement.

### Step 3: Calculate the number of arrangements
Thus, the number of ways to arrange \( n \) different objects at a round table is given by:
\[ (n-1)! \]

### Final Answer
Therefore, the number of ways in which \( n \) different objects can be arranged at a round table is \( (n-1)! \).

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