Publish Date: June 10, 2024

Permutation & Combinations

Permutations

Permutations are arrangements of items where the order matters. The number of permutations of items taken at a time is denoted as and can be calculated using the formula:

Example

Find the number of permutations of 5 items taken 3 at a time.

Given and :

Calculating factorials:

Therefore:

So, there are 60 ways to arrange 5 items taken 3 at a time.

Combinations

Combinations are selections of items where the order does not matter. The number of combinations of items taken at a time is denoted as and can be calculated using the formula:

Example

Find the number of combinations of 5 items taken 3 at a time.

Given and :

Calculating factorials:

Therefore:

So, there are 10 ways to choose 5 items taken 3 at a time without regard to order.