circular permutation

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ohwell: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Sat Aug 16, 2008 7:10 pm; Thanked: 1 times

circular permutation

by ohwell » Sat Nov 22, 2008 8:59 pm

Find the number of ways in which five persons can sit around a circular table, when two of the persons insist on sitting next to each other?

I went as far as drawing all the combinations and I reached at 10, but the answer is aparantly 12. Can anyone explain?

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Source: Beat The GMAT — Problem Solving | Sat Nov 22, 2008 8:59 pm

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; GMAT Score:730

Re: circular permutation

by logitech » Sat Nov 22, 2008 9:48 pm

ohwell wrote:Find the number of ways in which five persons can sit around a circular table, when two of the persons insist on sitting next to each other?

I went as far as drawing all the combinations and I reached at 10, but the answer is aparantly 12. Can anyone explain?

You should use (n-1)! to find the circular permutation.

The reason is you can sort N people in n! ways but for the n times you will have same combination with two different starters since they are in circle:

So : n!/n = (n-1)!

Since two people wants to sit next to eachother, the total group will act like 4 people

12 3 4 5

(4-1)! = 6 ways

but since they can also switch places:

21 3 4 5

6 x 2 = 12 ways.

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