Permutation

Definition

A permutation is an arrangement of all the members of a set into a specific sequence or order. The number of permutations of a set with $n$ distinct elements is given by $n!$ (n factorial).

5 Must Know Facts For Your Next Test

1. A permutation focuses on the arrangement where order matters.
2. The formula for the number of permutations of $n$ items taken $r$ at a time is $_nP_r = \frac{n!}{(n-r)!}$.
3. If there are duplicate items in the set, the number of unique permutations is reduced accordingly.
4. Permutations are often used in probability and counting problems to determine possible arrangements.
5. When calculating permutations, always ensure that you consider whether repetitions are allowed or not.

Review Questions

• What distinguishes a permutation from a combination?
• How would you calculate the number of permutations for 5 items taken 3 at a time?
• In how many ways can you arrange the letters in the word 'ALGEBRA'?

Related terms

Combination: A combination is a selection of items from a larger pool where order does not matter.

Factorial: The product of all positive integers up to a given number $n$, denoted as $n!$. For example, $4! = 4 \times 3 \times 2 \times 1 = 24$.

Sequence: An ordered list of numbers or objects, where repetition and order are both significant.