We took up our homework questions (and had a fire drill). Then we had a quiz (Permutations Quiz 1 – some identical items) which we looked at right away (remember, quizzes aren’t included in your grade).
We’re just starting to look at Combinations – choosing stuff instead of arranging stuff. Our example in class was something like this:
5 people volunteer to run the Tuck Shop. Only 2 people are needed. How many different pairs are possible?
There are 10 different pairs. If there were “first” and “second” people, then the order in which two people were chosen would matter (for example, Alfred-Bonnie would be a different pair than Bonnie-Alfred). This would give 20 pairs, but that doesn’t make sense for this situation. Since every pair has two “orders”, we divide 20 by 2 to get 10 unique pairs. This is a pretty small number, so you can just list the pairs to see this value.
Tomorrow we’ll generalize this and get a useful formula as well. Stay tuned!