No two evens adjacent

MediumCombinatorics~5m

How many permutations of {1,2,3,4,5,6,7}\{1, 2, 3, 4, 5, 6, 7\} have no two even numbers adjacent to each other?

Show hints (2)+
  1. Lay down the 44 odd numbers first (4!4! ways); they create 55 gaps.
  2. Drop the 33 evens into distinct gaps: 5435\cdot4\cdot3. Multiply.

Answer

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1440

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Asked at: Jane Street, Citadel

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