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dumpman
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Homework Statement
how many ways can 10 people sit around a roundtable if 3 particular people sit together
Homework Equations
The Attempt at a Solution
my attempt was (8-1)! x 3!
dumpman said:how many ways can 10 people sit around a roundtable if 3 particular people sit together
…
my attempt was (8-1)! x 3!
Dick said:But if you think circular rotations are not important you can go with Halls and tiny-tims answer.
A circular permutation problem is a type of combinatorial problem in which objects are arranged in a circle rather than a straight line. It involves finding the number of unique arrangements or combinations of objects in a circular order.
In a linear permutation problem, the order of objects in a straight line matters. However, in a circular permutation problem, the order of objects in a circle is considered the same as long as the relative positions of the objects are maintained. This means that rotations do not change the arrangement and are not counted as separate arrangements.
The formula for solving a circular permutation problem is n!/n where n is the number of objects. This is because in a circular permutation, n rotations of the same arrangement are considered the same. Therefore, we divide the total number of arrangements (n!) by the number of rotations (n) to get the unique arrangements.
One example of a circular permutation problem is arranging 5 people around a circular table. The number of unique seating arrangements would be 5!/5 = 24, as rotating the same arrangement would not change the overall seating arrangement.
Yes, circular permutation problems have various real-life applications, such as scheduling shifts for employees in a circular work setting, arranging seats in a circular theater, or organizing a round-robin tournament in sports. They are also commonly used in computer science for tasks such as generating unique passwords or shuffling elements in a circular array.