Permutation
A permutation counts the number of possible arrangements when order matters.
What is a permutation?
A permutation refers to an arrangement of objects in a specific order. In permutation problems, changing the order of elements creates a different outcome.
Permutation formula
The number of permutations of r items selected from n distinct items is given by:
nPr = n! / (n − r)!
Example
Suppose you have 4 letters: A, B, C, D
If you select and arrange 2 letters:
AB ≠ BA
Number of permutations = 4P2 = 12
If you select and arrange 2 letters:
AB ≠ BA
Number of permutations = 4P2 = 12
When does order matter?
Order matters in situations such as rankings, seating arrangements, passwords, and codes. If changing the order changes the result, then permutations should be used.
Permutation vs combination
Permutations consider order, while combinations do not. If order is irrelevant, combinations are the appropriate method.
Why are permutations important?
Permutations are widely used in probability theory, statistics, computer science, and operations research to count possible outcomes.