SOLUTION: In how many ways can 6 people be arranged so that they form a circle between them; and if 2 particular people of the 6 people quarell, how many arrangements must be made if the qua
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Question 1134223: In how many ways can 6 people be arranged so that they form a circle between them; and if 2 particular people of the 6 people quarell, how many arrangements must be made if the quarellsome pair must not stand next to each other? Answer by ikleyn(52798) (Show Source):
You can put this solution on YOUR website! .
(a) In how many ways can 6 people be arranged so that they form a circle between them;
(b) and if 2 particular people of the 6 people quarrel, how many arrangements must be made if the quarrelsome pair
must not stand next to each other?
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Pay attention on how I edited your post to separate and clearly show that there are TWO QUESTIONS here.
(a) There are = (n-1)! circular arrangements of n objects.
In this case n = 6, so there are (6-1)! = 5! = 120 circular arrangements of 6 persons.
(b) Among these 120 circular arrangements, there are ONLY TWO, where the opponents are neighbors.
So, the answer to question (b) is 120 - 2 = 118 circular arrangements.
