I would like you to help me with one example. There are eight people(A,B,...,H). In how many ways can eight people, denoted A,B,.....,H be seated around the square table? The result is $10,080$ possible ways. I've also found three possible ways how to solve this example but I still can't get it.
The first method is 8!/4. Why do we have to divide by $4$ ?
The second method is 7! x 2. Why do we have to multiply by $2$ ?
- The last method is following: In how many ways can i split these eight people to four groups of two? The last method is clear to me, but I do not know how to calculate it. Can you help me ?