Permutation Formula

The permutation formula is used to find the number of ways objects can be arranged when the order matters. It is commonly used in probability, counting problems, and mathematics.

Permutation Formula

The formula for arranging r objects from a total of n objects is:

nPr = n! / (n − r)!

Here, n is the total number of objects, r is the number of objects being arranged, and ! represents factorial.

Example of Permutation

Suppose you have 5 different books and want to arrange 3 of them on a shelf. The number of possible arrangements is:

5P3 = 5! / (5 − 3)!

= 5! / 2!

= (5 × 4 × 3 × 2 × 1) / (2 × 1)

= 60

So, there are 60 different arrangements.

Permutation vs Combination

The main difference is that permutations consider order, while combinations do not. For example, ABC and BAC are different permutations because their order is different.

When to Use the Permutation Formula

Use the permutation formula when you are selecting or arranging items and the order of those items matters. It can be useful for seating arrangements, rankings, passwords, schedules, and other counting problems.