SOLUTION: seven boys and seven girls went to watch a movie. How may ways can they be seated if grace and joey are members of the group and want to sit together all the time?

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Question 722523: seven boys and seven girls went to watch a movie. How may ways can they be seated if grace and joey are members of the group and want to sit together all the time?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Think of Grace and Joey as one person that take up one "seat" since they cannot be separated. So you really have 14 - 2 + 1 = 13 people.

There are 13! = 13*12*11*10*9*8*7*6*5*4*3*2*1 = 6,227,020,800 ways to arrange the 13 people

Double this to get 2*6,227,020,800 = 12,454,041,600 ways total

Note: you double it because there are 2 ways to arrange Grace and Joey