Permutations Explained
Permutations are the number of ways to arrange a set of objects where order matters.
Permutation Formula
The number of permutations of \(n\) distinct objects is:
\[ P(n) = n! \]
Where \(n! = n \cdot (n-1) \cdot (n-2) \cdots 1\).
Example
How many ways to arrange 3 letters: A, B, C?
\[ P(3) = 3! = 3 \cdot 2 \cdot 1 = 6 \]
Arrangements: ABC, ACB, BAC, BCA, CAB, CBA.
Applications
Permutations are used in scheduling (e.g., race lineups), coding (e.g., password generation), and optimization problems.