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Counts ordered arrangements of r items chosen from n. Order matters โ choosing ABC is different from choosing BAC.
The total number of permutations of a 9ร9 Sudoku puzzle (before constraints) is P(81,81) = 81! โ 5.8ร10ยนยฒโฐ โ but valid Sudokus number only about 6.7ร10ยฒยน.
Using permutations when order doesn't matter โ "choose 3 toppings from 10" is a combination, not a permutation. C(10,3) = 120, not P(10,3) = 720.