# Permutations (_{n}P_{r})

How to solve permutation problems (and factorials): formula, examples, and their solutions.

## Example 0: Factorial

5! (5 factorial) means multiply from 5 to 1.

5! = 5⋅4⋅3⋅2⋅1

## Example 1

_{7}P_{3} means multiply from 7 to 3 numbers._{7}P_{3} = 7⋅6⋅5

## Example 2

_{4}P_{4} means multiply from 4 to 4 numbers._{4}P_{4} = 4⋅3⋅2⋅1

This is equal to 4!._{n}P_{n} = *n*!

## Example 3

_{5}P_{1} means multiply from 5 to 1 number, itself._{n}P_{1} = *n*

## Example 4

_{n}P_{0} = 1

## Example 5

From 9 students,

you select 4 students

and arrange them **in order**.

So this is a permutation problem.

So the answer is _{9}P_{4}.

## Example 6

From 8 numbers,

you select 3 numbers

and arrange them **in order**.

So this is a permutation problem.

So the answer is _{8}P_{3}.

## Example 7

From 5 numbers,

you select 5 numbers

and arrange them **in order**.

So this is a permutation problem.

So the answer is _{5}P_{5} or 5!.