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This question is only for Aryabhatta/STARS
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There are 6 gentlemen and 3 ladies to sit around a circular table. In how many ways they seat themselves so that
(1) Every gentleman have lady on its adjacent.
(2) Two particular ladies refused to sit beside a particular gentleman.
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Answers
Answer:
(1) Every gentleman have lady on its adjacent
=> Start out by seating the men at the table…put six chairs down and sit the six me in them. Circular table seating says there are (6–1)! = 5! = 120 ways to do so.
Now, the ladies’ seating is another circular table problem, so there are (3–1)! = 2! = 2 ways to seat the ladies.
Put it together: 5!2! = 120*2 = 240 total such arrangements.
(2) Two particular ladies refused to sit beside a particular gentleman.
=> The number of ways of arranging n things around a table is (n-1)!
Now, we will seat the 6 men around the table first. The number of arrangements is (6–1)! = 5! ways.
Let the men be termed M1, M2, M3, M4, M5 and M6. There are totally 6 places between each pair of men. Since filling up of these vacancies becomes a linear arrangement, the 3 ladies can be seated in between the gentlemen in one way.
Hence, the number of ways of seating 3 ladies and 6 gentlemen round a table so that no two ladies sit together is 5! (1!) = 120
Answer:
Check the attachment!!!
