An inversion of a permutation σ is a pair (i,j) of positions where the entries of a permutation are in the opposite order: i σj. So a descent is just an inversion at two adjacent positions. For example, the permutation σ = 23154 has three inversions: (1,3), (2,3), (4,5), for the pairs of entries (2,1), (3,1), (5,4). Sometimes an inversion is defined as the pair of values. A typical combination lock for example, should technically be called a permutation lock by mathematical standards, since the order of the numbers entered is important; 1-2-9 is not the same as 2-9-1, whereas for a combination, any order of those three numbers would suffice. = 7 x 6 x 5 x 4 x 3 x 2 x 1 7! = 5,040 Calculate our permutation value n P r for n = 12 and r = 5: 12 P 5 =. 12 P 5 = 95,040. In Microsoft Excel or Google Sheets, you write this function as =PERMUT(12,5) For More Information, Check Out Permutations and Combinations Flashcards Below. Permutations and Combinations Video.
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