Question 876801: There are 6 children and husband/wife have to be in the middle. How many ways can they be seated?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let's say we have these 8 people: A,B,C,D,E,F,G,H
Let A and B be the husband and wife. Consider them as one person. Call this "person" Z
So we now have this group Z,C,D,E,F,G,H
"Person" Z has to be in the middle, so let's force Z to be in slot 4 to get C,D,E,Z,F,G,H
Z is locked in slot 4 and cannot move. There are 7-1 = 6 other slots. So there are 6! = 6*5*4*3*2*1 = 720 ways to arrange them.
Because we can arrange the husband and wife to be on either side of each other (to have AB or BA) we need to double 720 to get 2*720 = 1,440
So there are 1,440 ways to seat this group of 8 people.
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