Permutation Calculator

Calculate permutations (nPr) to find the number of possible arrangements.

Understanding Permutations

Permutation is the arrangement of objects in a specific order. It is used when the order of selection matters. For example, finding the number of ways to arrange books on a shelf or selecting teams with specific roles.

$$P(n, k) = rac{n!}{(n-k)!}$$

n is the total number of items available.
k is the number of items to be chosen and arranged.
P(n, k) represents the number of permutations of n items taken k at a time.
! denotes factorial, the product of all positive integers up to that number.

Total items (n):

Items to choose (k):

Result:

What are Permutations?

In mathematics, a permutation is an arrangement of objects in a specific order. The number of permutations of n distinct objects taken k at a time is denoted by P(n, k) or ⁿP_k. It is calculated using the formula:

$$P(n, k) = rac{n!}{(n-k)!}$$

Where:

n is the total number of distinct objects.
k is the number of objects to be arranged, where k ≤ n.
n! (n factorial) is the product of all positive integers up to n.

Permutations are different from combinations, where the order of selection does not matter. Permutations are used in various fields such as probability, statistics, and computer science to count the number of possible arrangements or sequences.

Example:

Suppose you have 5 books and you want to arrange 3 of them on a shelf. How many different arrangements are possible?

Here, n = 5 (total books) and k = 3 (books to arrange).

Using the permutation formula:

$$P(5, 3) = rac{5!}{(5-3)!} = rac{5!}{2!} = rac{120}{2} = 60$$

So, there are 60 different ways to arrange 3 books out of 5 on a shelf.

Sources: Wikipedia, MathWorld