key term - Permutation

Definition

A permutation is an arrangement of all or part of a set of objects in a specific order. The order of the elements is crucial, and changing the order produces a different permutation.

5 Must Know Facts For Your Next Test

1. A permutation considers the arrangement of objects where order matters.
2. The number of permutations of n distinct objects taken r at a time is given by $P(n, r) = \frac{n!}{(n-r)!}$.
3. For n distinct objects, the total number of permutations is $n!$ (n factorial).
4. If some objects are identical, the formula for permutations adjusts to account for these repetitions.
5. Permutations are used in counting principles to determine possible outcomes in probability scenarios.

Review Questions

Related terms

Combination:

An arrangement or selection of items where order does not matter.

Factorial:

The product of all positive integers up to a given number, denoted as n!. For example, $5! = 5 \times 4 \times 3 \times 2 \times 1$.

Counting Principle: A fundamental principle used to count the number of ways multiple events can occur, often involving multiplication.