Question

How many ways can we arrange 4 boys around a circular table?

Answer 1

Answer:

6

Step-by-step explanation:

Method 1

Since the table is circular, we consider arrangements to be "the same" if they're related by rotating around the circle.

So with a suitable rotation, we may suppose that boy number 1 is in a particular seat.

There are then 3! = 6 ways to arrange the remaining 3 boys in the remaining seats.

Method 2

There are 4! ways to assign the 4 boys to the 4 positions, but allowing for rotations, this counts each "essentially different" arrangement 4 times.  So the total number of arrangements is 4! / 4 = 3! = 6.