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Consider all permutations of the integers 1,,1000. In how many of these permutations does 1 appear before 2, 2 appear before 3, and 3 appear
Consider all permutations of the integers 1,,1000.
- In how many of these permutations does 1 appear before 2, 2 appear before 3, and 3 appear before 4? (In other words, 1,2,3,4 appear in order, but not necessarily consecutively.)
- In how many of these permutations do 1,2,3,4 appear in order but no two are adjacent?
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