Combination Formula

Combination

Formula

Summary

The combination formula describes the possible combination of elements out of a group of elements. In combinations, order does not matter. See the formula for permutations for where order does matter.

Expression Description
The total number of elments in the group
The number of elements to select

Usage Notes

The combination formula describes the possible combination r elements out of a group of n elements where order does not matter.

Examples

4 Choose 3 Order Does Not Matter

To calculate four choose three where order does not matter, you can use the formula for n choose r combinations. For example if we want to calculate the possible combination of choosing three items from the set {♥︎,♦︎,♣︎,♠︎} we can set up the formula:

First we substitute four in for the variable to represent the size of the set. Then we substitute three for the variable to represent the number of items we are choosing.

To double check our work, we can display the four unique combination of these three items. Note, if order does matter, you can use the formula for permuations.

  1. { ♣︎, ♦︎, ♥︎ }
  2. { ♣︎, ♦︎, ♠︎ }
  3. { ♣︎, ♥︎, ♠︎ }
  4. { ♦︎, ♥︎, ♠︎ }
Steps
4 Choose 2 Order Does Not Matter

To calculate four choose two where order does not matter, you can use the formula for combinations. For example if we want to calculate the possible combinations of choosing twp items from the set {♥︎,♦︎,♣︎,♠︎} we can set up the formula:

First we substitute four in for the variable , representing the size of the set. Then we substitute two for the variable , representing the number of items we are choosing.

To double check our work, we can display the six possible permutations of these two items chosen from the set. Note, if order does matter, you can use the formula for permuations.

  1. { ♥︎, ♠︎ }
  2. { ♦︎, ♠︎ }
  3. { ♥︎, ♦︎ }
  4. { ♣︎, ♠︎ }
  5. { ♥︎, ♣︎ }
  6. { ♣︎, ♦︎ }
Steps