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.
Hi,
The keywords are "bearing in mind the condition in (i)", so there are two restrictions we will need to take into account. Thus, we will not have 8 spaces to slot in 2 absentees.
Cheers,
Wen Shih
I tried to split them into cases, however, I still couldn't get the correct answer. A little help please?
Just realised you missed out saying that there are a total of 8 friends at the first part of the question.
"A group of friends sit together in a circle."
Should be "A group of 8 friends sit together in a circle."
oops sorry.. my mistake.. any helpers?