How to Calculate Combinations & Permutations in R


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

#calculate total combinations of size r from n total objects
choose(n, r)

#calculate total permutations of size r from n total 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 size 2 from 4 total 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 size 2 from 4 total 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.

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