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A permutation, in combinatorics, is a sequence of elements in which no element appears twice. In a sequence, unlike in a set, the order in which the elements are written down matters. Suppose you have a total of n distinct objects at your disposal and you want to create permutations of k elements selected from those n, where k≤n. |
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In combinatorics, a permutation is a sequence of elements in which no element appears more than once. In a sequence, unlike in a set, the order in which the elements are written down matters. Suppose you have a total of n distinct objects at your disposal and you want to create permutations of k elements selected from those n, where k≤n. |
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by nPk and use the factorial notation, we can write :nPk = n! / (n-k)! |
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by P(n, k) and use the factorial notation, we can write :P(n, k) = n! / (n-k)! |
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Two permutations of a set of n elements (often, {1, 2, 3, ..., n}) can be composed, i.e. applied successively to the set. For instance, if a = (125)(34), and b = (13)(2)(45), applying b after a maps 1 to 2, and then to itself; 2 to 5 to 4; 3 to 4 to 5, and so on. So composing b and a gives ba = (124)(35). |
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Two permutations of a set of n elements (often, {1, 2, 3, ..., n}) can be composed, i.e. applied successively to the set. For instance, if a = (125)(34), and b = (13)(2)(45), applying b after a maps 1 to 2, and then to itself; 2 to 5 to 4; 3 to 4 to 5, and so on. So composing b and a gives ba = (124)(35). It is a matter of notation whether applying a and then b is to be denoted by ba (as here) or by ab: the first convention agrees with a functional notation (ba(2) meaning b(a(2)) ); the second one with an exponential notation (2ab = (2a)b). |
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