Couples
Five couples (one man, one woman) come into a restaurant and they all sit at at long rectangular table. They all only sit on the long sides, not the shorter sides. Each couple sits either directly across from each other, or right next to each other. How many ways can the couples be seated at the table?
(The table has 5 seats on each of the long sides, and each person must sit in one of those seats)
The answer is 30720.
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There are 8 ways to put 5 identical 2x1 dominoes into a 2x5 slot.
If the dominoes are distinguishable, there are 8x5! ways to arrange them.
If each dominoes are a combination of male and female, there are 8x5!x(2x2x2x2x2) = 30720 ways to arrange them.