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