SOLUTION: Four married couples have bought eight seats in a row for a basketball game. In how many ways can they be seated if each couple is to sit together?

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Question 1006235: Four married couples have bought eight seats in a row for a basketball game. In how many ways can they be seated if each couple is to sit together?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the seats are numbered:
1, 2, 3, 4, 5, 6, 7, 8
Now group them in pairs:
1 2, 3 4, 5 6, 7 8
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There are 4 couples that can occupy ( 1 2 )
After a couple is placed there, there are
3 couples that can occupy ( 3 4 ), and so on
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+4%2A3%2A2%2A1+=+24+ are the ways couples can be seated
but they can be ( male female ) or ( female male ),
so there are +2%2A2%2A2%2A2+=+16+ ways to do this, so
+24%2A16+=+384+ different ways the couples can be seated