In 10080 ways
Step-by-step explanation:
We first treat the two people how have to sit together as 1 item taking up 2 seats so they have 7 possibilities of seats i.e. 12 23 34 45 56 67 78 and the two of them can sit in 2 possible ways, AB or BA
Now, the other 6 people will have 6 seats to choose from. So the total number of ways they can sit is 6 for the first person 5 for the second and so on so its 6!
Thus, the total number is [tex]7 \times 2 \times 6 ![/tex] = 10 080
