Lesson 4

In the Permutations and Combinations gizmo, you may have noticed you could represent the number of combinations 5C3 as The number of combinations, nCr, is equal to the number of permutations, nPr, divided by the number of ways the elements could be arranged, r!.

In the Two Scoops example, you saw 2!, or 2, duplicates for each cone, so there were twice as many permutations as combinations. So to find the combinations, divide nPr by 2! in order to remove the duplicates.

Your calculator likely has a nCr button that will calculate the number of combinations for you. Note that some textbooks use an alternate notation for combinations where

For the previous ice cream example, you could write and know this meant 4C2. You evaluated this and got 6. The combination function on your calculator will likely be found in the same menu as the permutation function. Make sure you can use your calculator to evaluate this. Check with your teacher if you have trouble finding this function.

Self-Check 1

A Grade 12 class of 120 students is forming a graduation committee.

1. In how many ways can a committee of 10 be chosen? Use two notations to represent your answer. Answer
2. Determine the numeric value of the representations from question 1. Answer
3. Explain why 120P10 is divided by 10! in the formula to find 120C10. Answer