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Permutations

A permutation involves rearranging the elements of a set in a situation where order is important. For example, there are 6 ways to permute the set \( \{ 1, 2, 3 \} \): \( (1,2,3), (1,3,2), (2, 1, 3), (2,3,1), (3,1,2), (3,2,1) \).

In general, there are \( n! = 1 \times 2 \times 3 \times \dots \times n \) ways to permute a set of \( n \) elements, and \( \frac{n!}{(n-k)!} \) ways to permute \( k \) elements of an \(n\)-sized set.

Note by Arron Kau
3 years, 1 month ago

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