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In how many ways can we seat 6 people around a round table if Fred and Gwen and Scott insist on sitting next to each other? (Two seatings are considered equivalent if one is a rotation of the other.)

 Jul 16, 2022
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tie Fred Gwen and scott together in a line.  there are 3! arrangements for this 

Now put them in the circle, they determine the 'start' of the pattern

There are 3 more people which can be arranged in 3! ways

 

So the answer is  3!*3!

 Jul 16, 2022

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