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
The following tutorials explain how to perform other common tasks in R:
How to Perform Linear Interpolation in R (With Example)
How to Select Unique Rows in a Data Frame in R
How to Replicate Rows in Data Frame in R