No proof for feedback, because there’s a test.
- Study for your test on Wednesday. You can hand in some practice problems on canvas. Resources/info:
- Test will be 20 minutes at the end of class, on counting problems. The problems will be short-answer problems (not proofs), grades mainly based on getting the answer correct.
- Materials from class are all available under “Materials Archive” tab. In particular, the main topics are:
- Multiplication, addition, subtraction, and division principles
- How to count all sorts of things by use of the principles above
- How to count the number of ways to order k elements chosen from n elements (and why it works)
- How to count the number of subsets of a set of size n (and why it works)
- How to count the number of subsets of size k chosen from a set of size n (binomial coefficient and its formula and why it works)
- Here are some example test problems I’ve given in the past. For hints, discuss on discord (use the “spoiler” feature on discord if hinting/spoiling anything). For full solutions, see this solution set. BUT I suggest you use the full solutions only when you are confident you have solved it yourself — asking for a hint is a better way to proceed for more effective learning.
- Hammack chapters 3.1-3.4 exercises are excellent practice.