Someone please help me with this question.
A group of friends sit together in a circle. Alice, Betty and
Candy are 3 members of the group of friends.
(i) If Alices refuses to sit beside Betty unless Candy sits on
the other side of Alice as well, how many arrangements can there
be?
Ans: 3840
I could get this one by adding up 3 cases- Alice with Betty and
Candy beside her, Alice with Candy and another friend beside her
and Alice with 2 other friends beside her.
What I could not get is the next part of the question
(ii) 2 latecomers then come to join the group and they have to
sit apart from each other. How many possible arrangements can there
be, bearing in mind the condition from (i)?
Ans: 212160
Seems that it's not as simple has slotting the 2 into 8
spaces.