2n(n−1)! ways n couples around a circular table such that no couple sits next to each other.
What is combination?
- The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant."
- Combining these two words indicates "Selection of things," where the order of the items is irrelevant.
Depends on how you consider two ways as different ways.
- If the seats are in fixed positions, then there are two possible seatings as the couple can swap with each other. In this case, choose a seat as reference.
- Swapping is available in each couple or between couples, on seat 0 and 2N sit one couple or different couples. So the answer is 2n+1n!
- If you consider seats as all same, pick a couple as reference. Still, husband can sit either on clockwise of his wife or counterclockwise.
- The remaining n−1 couples can choose their seats at will. In this case the answer is 2n(n−1)! when n>1. When n=1 there’s only 1 since the relative position becomes unimportant in this case.
In case you still feel confused, take 2 for example. We have plan AaBb, AabB, aABb and aAbB
To know more about combinations check the below link:
https://brainly.com/question/11732255
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