In “Permutations and Combinations” you may have noticed that 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 Two Scoops, you saw 2!, or 2, duplicates for each cone, so there were twice as many permutations as combinations.

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
In Two Scoops you could have written and known that this meant 4C2. You evaluated this equation 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 evaluate combinations and permutations using your calculator. Check with your teacher if you have trouble finding these functions.

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. What is the total number of 10-person committees that can be formed? Answer
3. Explain why 120P10 is divided by 10! in the formula to find 120C10. Answer