Permutations (nPr)

Permutations (nPr)

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

Example 0: Factorial

Evaluate the given number: 5!.

5! (5 factorial) means multiply from 5 to 1.
5! = 5⋅4⋅3⋅2⋅1

Example 1

Evaluate the given number: 7P3.

7P3 means multiply from 7 to 3 numbers.
7P3 = 7⋅6⋅5

Example 2

Evaluate the given number: 4P4.

4P4 means multiply from 4 to 4 numbers.
4P4 = 4⋅3⋅2⋅1
This is equal to 4!.

nPn = n!

Example 3

Evaluate the given number: 5P1.

5P1 means multiply from 5 to 1 number, itself.

nP1 = n

Example 4

Evaluate the given number: 3P0.

nP0 = 1

Example 5

There are 9 students in a class. How many ways are there to select 4 students and arrange them in a row?

From 9 students,
you select 4 students
and arrange them in order.

So this is a permutation problem.

So the answer is 9P4.

Example 6

By using numbers {1, 2, 3, 4, 5, 6, 7, 8} once, how many 3-digit numbers can be made?

From 8 numbers,
you select 3 numbers
and arrange them in order.

So this is a permutation problem.

So the answer is 8P3.

Example 7

By using numbers {1, 2, 3, 4, 5} once, how many 5-digit numbers can be made?

From 5 numbers,
you select 5 numbers
and arrange them in order.

So this is a permutation problem.

So the answer is 5P5 or 5!.