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8. Calculating Combinations
Combinations are a related concept to permutations, where the order of the selected items is not important. Learn how to calculate combinations in this lesson.
Lesson Goal (00:10)
The goal of this lesson is to learn how to calculate combinations.
Understanding Combinations (00:16)
A combination is a selection of items from a set, where the order of the items is not important. This differs from a permutation, where the order is important. As a result, a single combination of items can contain multiple permutations.
Calculating Combinations (01:15)
To determine the number of combinations for a problem, we can determine the number of permutations, then divide by the number of permutations in each combination.
In our example, we are finding the number of combinations of 3 people that can be selected from a set of 7 people. This calculation is written as 7C3. We previously found the number of permutations is 210. The number of permutations for a selection of 3 people is 3!, which is 6. As a result, the number of combinations is 210 divided by 6 which is 35.
A Formula for Combinations (03:02)
In the previous lesson, we identified a general formula for calculation permutations. We can modify this to create a formula for calculating nCr for any numbers n and r. To do this, we divide the permutation formula by r!, which is the number of permutations in a combination. As a result, we can calculate nCr by dividing n! by r! multiplied by (n-r)!