Keeping two apart

MediumCombinatorics~4m

Five people stand in a row. In how many arrangements are two specific people not next to each other?

Show hints (2)+
  1. Count the complement: arrangements where they ARE adjacent.
  2. Glue the pair into one block (×2 for internal order), then subtract.

Answer

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72

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Asked at: Jane Street, Citadel

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