One Fancy Night
A family of 8 members, consisting of the father, the mother, 3 sons and 3 daughter went for a fancy dinner and ate on a round table. If the father and mother were to be seated together, how many ways could the family be seated?
As it is a round table, rotations are considered the same arrangement.
image credit: Wikipedia Ramon FVelasquez
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Since this involves round tables, the formula for this kind of permutation is:
(n-1)!
But since the couple (husband and wife) were seated together, both of them will be counted as one.
Therefore, 7 is the value of n instead of 8.
(7-1)! = 6! = 720
Looking back to the couple. It only said that they should be seated together. But it does not say that they cannot interchange places. This condition is represented as 2! or simply 2.
720 X 2 = 1 440
Therefore, 1 440 is our final answer. :)