Permutations

Definition

Permutations are arrangements of objects in a specific order. The order of the objects is crucial and changing the order creates a different permutation.

5 Must Know Facts For Your Next Test

1. The number of permutations of n distinct objects is n! (n factorial).
2. Permutations where some objects are repeated use the formula n! / (n1! * n2! * ... * nk!), where ni are the frequencies of the repeated elements.
3. Permutations differ from combinations because permutations consider order while combinations do not.
4. The notation P(n, r) represents the number of ways to arrange r objects out of n total objects.
5. In probability, permutations are used to calculate outcomes where sequence or arrangement matters.

Review Questions

• How do you calculate the number of permutations for arranging 5 distinct objects?
• What is the difference between permutations and combinations?
• If you have a set with repeated elements, how does this affect your permutation calculation?

Related terms

Factorial: The product of all positive integers up to a given number, denoted as n!.

Combination: A selection of items without considering the order, often represented as C(n, r).

Probability: The measure of how likely an event is to occur, often expressed as a fraction or percentage.