Answer:
3600
Step-by-step explanation:
Given that there are 8 people to be seated around a circular table.
As per formula:
Number of ways that they n people can sit around a circular table = [tex](n-1)![/tex]
We know that 2 people of out of these 8 are not allowed to sit together.
If we subtract the number of ways of these 2 people sitting together from the total number of ways of sitting of 8 people, we will get the number of ways that these 2 people do not sit together.
Number of ways of 2 people not sitting together = Total number of ways of 8 people sitting - Number of ways these 2 people sitting together.
Using formula:
Total number of ways = [tex](8-1 )! = 7! = 5040[/tex]
Let these two people always sit together, so these 2 can be thought as one pair.
So, 6 people and 1 pair,
Total number of ways the 2 people sitting together = [tex](7-1)! \times 2 = 6! \times 2 = 720 \times 2 =1440[/tex]
Total number of ways that the two do not sit together =
[tex]5040 - 1440\\\Rightarrow 3600[/tex]
