Circular Table Conference

Probability Level 3

Six people sit down around a circular table. This group of six people includes a pair of identical twins. How many ways can the six people be seated?

Note : Two seatings are considered the same if one can be rotated to form the other. Two seatings are also considered the same if the two twins switch positions.


The answer is 60.

Tushar Malik by Tushar Malik , 20, India

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2 solutions

Sudoku Subbu
Feb 15, 2015

The no. of ways of arranging 6 people around a circular table is ( 6 − 1 ) ! = 5 ! = 120 (6-1)!=5!=120 and also given that clockwise and anti clockwise are the same so the no of ways is 120 2 = 60 \frac{120}{2}=60

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It is 120/2 and not 60/2 . Also the answer is 60 not 30.

Tushar Malik - 6 years, 3 months ago

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Yesi have written the same what is your probllem

sudoku subbu - 6 years, 3 months ago

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Earlier u had written 60/2 = 30 as the answer.

Tushar Malik - 6 years, 3 months ago
Tushar Malik
Feb 15, 2015

There are 6!=720 ways to seat the six people. For any seating, there are 6 ways to rotate it around the table, so we divide by 6 to get 720/6=120. Also, we can switch the twins, so we divide further by 2, to get a count of 120/2= 60 .

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