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

• What is the difference between a permutation and a combination?
• How do you calculate the number of permutations of 5 objects taken 3 at a time?
• If you have 4 letters and two are identical, how does this affect the number of unique permutations?

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.