Circular Arrangements- What's wrong with my working? (1 Viewer)

[bleh1234]

Find the number of ways of seating 10 people around a table if three people are to sit together.
The answer is 4320, but i got 30240.
I did:
Let the 3 people be one group. Therefore, there are 8 groups.
Total arrangements of groups x arranging the 3 people in the one group
(8-1)! x 3! = 30240.
Thanks very much

 

[SilentWaters]

4320 is wrong, it's short by a factor of 7 (and I think it assumes there are 6 distinct groups being arranged, rather than 7). Your answer's right.

 

[bleh1234]

Thank you!
I'm not sure if anyone will see this but i have another permutations question. (i feel annoying starting a new thread)
Any help is appreciated:
How many different arrangements are possible if 3 letters are randomly selected from the word CHALLENGE and arranged into ‘words’?

 

[FrankXie]

case (i) three letters all different:7p3
case (ii) two alike one different: 2c1 times 6c1 times 3!/2!
then sum up

 

[mrpotatoed]

SilentWalters is wrong, your working would be right if they were arranged in a line. For a circle you have to divide your answer by the number of groups (7)... hence the answer in the book.

 

[braintic]

SilentWalters is wrong, your working would be right if they were arranged in a line. For a circle you have to divide your answer by the number of groups (7)... hence the answer in the book.

No, I am afraid you are wrong.
The division by 7 has already been accounted for, because the three neighbours have only been ordered, not placed in three specific seats.