SOLUTION: How many ways are there to seat four of a group of ten people around a circular table where two sitting are considered the same when everyone has the same immediate left and immedi

Question 672505: How many ways are there to seat four of a group of ten people around a circular table where two sitting are considered the same when everyone has the same immediate left and immediate right neighbour?
Answer by chandrumail(4) (Show Source): You can put this solution on YOUR website!
The 4 people can be chosen from the group of 10 in 10C4 ways =
10*9*8*7/(4*3*2*1) = 210 ways
Since it's a circular arrangement, Each of the 210 different choices of 4 people can be arranged in (4-1)! ways
Everyone has the same immediate left and immediate right neighbour means the clockwise and anticlockwise arrangement are not same.

So, total number of ways = 210*3! = 210*6 = 1260 ways

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