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Neighbours in a row
distinct traders sit in a row of chairs. of them, who share a desk, must sit next to each other. How many seating orders are possible?
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Hint
Glue the neighbours into one block and arrange the blocks first.
Solution
- Glue the neighbours into one block, which leaves units to arrange.
- The units can be ordered in ways.
- Inside the block the traders can swap places, which gives a factor of .
- Multiplying gives seatings.
- Hence the number of seatings is .
Answer: