1. Warm up!If you flip a coin 6 times, how many different outcomes are there?

2. And for your exams… …the average was a 76%… …the median was a 84%… …and on average, students lost CRAZY points on questions 9-17.

3. The Wørd

4. Section 8.6 Counting Principles

5. Slips of paper with the numbers 1-20 inclusive are placed into a hat. How many ways can you pick an odd number? So I have only taught this… A prime number? A prime or an odd number?

6. An integer divisible by 5? …twice in seven years of teaching. Two integers whose sum is 8? Slips of paper with the numbers 1-20 inclusive are placed into a hat.

7. Permutations A permutation of n things is an ordering of the elements such that ORDER MATTERS, and there is a first, second, third, and so on. Here is time number three… But there’s an easier way to think about these…

8. In how many different ways can a 10 question MC exam be answered if each question has 5 answers? …and I really hope…

9. There are five people waiting in line for one bathroom. In how many different ways can they go #2? …I don’t screw this up too badly.

10. You’re at Six Flags with three friends. You’re all going to ride the Log thingie at the same time, but you’re the only one that won’t sit in front. In how many ways can you all sit in the log? I’m actually a li’l jealous of Hopkins…

11. The state of Missouri has license plates that consist of three letters and then three numbers. How many different license plates can the state have? …not only because she has much more experience teaching this…

12. Distinguishable Permutations Suppose a set of n objects has n 1 of one kind of objects, n 2 of a second kind, n 3 of a third and so on. The number of distinguishable permutations is: …but also because she owns Settlers of Cattan.

13. In how many distinguishable ways can the letters in the word “Google” be written? I can’t think of a better way…

14. …to learn and practice probability… In how many distinguishable ways can the letters in the word “Parallelogram” be written?

15. …than by playing a board game. Combinations The number of combinations of n things taken r at a time is given by:

16. And even better yet… Five people are running for three spots on a school committee. How many different committees are possible?

17. …Settlers is not just any board game. How many different five card poker hands are possible?

18. It’s a game of strategy, deceit, and betrayal. So how do you know when to use a Permutation or a Combination?

19. I’m pretty good at all of those things… 8 boys and 6 girls are applying to be in Mr. Wu’s Super-Awesome Club. If he can only take 4 guys and 4 girls, how many different ways can Mr. Wu select his club members?

20. …especially the deceit and betrayal. You are playing Risk, and rolling 5 dice at the same time. How many possible outcomes are there?

21. And there are few things in life… How many different distinguishable permutations are there of the word basketball?

22. …better than lording a Settlers win… You are playing a game that requires you to drawr two cards from a deck, roll one dice, and flip two coins. How many outcomes are there?

23. …over one of your mortal enemies. You are trying out for the first ever PSH co-ed cricket team. Thirty other students are also trying out, and the roster has a limit of 16 players. How many different teams are possible?

24. 8.6: from the packet! And your homework!