You can use the following functions to calculate combinations and permutations in R:

#calculate total combinations of sizerfromntotal objects choose(n, r) #calculate total permutations of sizerfromntotal objects choose(n, r) * factorial(r)

The following examples show how to use each of these functions in practice.

**Example 1: Calculate Total Combinations**

**Combinations** represent ways of selecting a sample from a group of objects in which the *order of the objects does not matter*.

For example, suppose we have a bag of four marbles: red, blue, green, and yellow. Suppose we’d like to select two marbles randomly from the bag, without replacement.

Here are the different combinations of marbles we could select:

- {red, blue}
- {red, green}
- {red, yellow}
- {blue, green}
- {blue, yellow}
- {green, yellow}

There are **6** total combinations.

Here is how to calculate the total number of combinations in R:

#calculate total combinations of size2from4total objects choose(4, 2) [1] 6

Our answer matches the number of combinations that we calculated by hand.

**Example 2: Calculate Total Permutations**

**Permutations** represent ways of selecting a sample from a group of objects in which the *order of the objects does matter*.

For example, suppose we have a bag of four marbles: red, blue, green, and yellow. Suppose we’d like to select two marbles randomly from the bag, without replacement.

Here are the different permutations of marbles we could select:

- {red, blue}, {blue, red}
- {red, green}, {green, red}
- {red, yellow}, {yellow, red}
- {blue, green}, {green, blue}
- {blue, yellow}, {yellow, blue}
- {green, yellow}, {yellow, green}

There are **12** total permutations.

Here is how to calculate the total number of permutations in R:

#calculate total permutations of size2from4total objects choose(4, 2) * factorial(2) [1] 12

Our answer matches the number of permutations that we calculated by hand.

**Additional Resources**

You can use the Combination and Permutation Calculator to automatically calculate the total number of combinations and permutations for a given sample size.