Intro Stats - Counting Activity

This semester, whenever possible, I have been trying to incorporate the flipped classroom in all of my courses. A couple of weeks back I used an activity that I was quite pleased with. It covered counting principles in introductory statistics, namely the multiplication principle, permutations, and combinations. Without having covered any of the material in class, I assigned my students to watch a short video I created on the subject. I placed the video on YouTube. Here it is.



There was also a short assignment that students had to complete before returning to class the next day. Here are the 5 questions.
1) An ice cream store has 31 flavors of ice cream and 3 types of cones. In how many different ways could you order a single-scoop ice cream cone? (1 flavor, 1 type of cone)
2) Which is the correct answer to the following problem: 10P2 or 10C2? A softball league has 10 teams in it. In how many different ways could the teams finish first and second?
3) Which is the correct answer to the following problem: 19P3 or 19C3? Bruce Springsteen has released 19 CDs. In how many different ways could a fan select 3 of his CDs to bring on a road trip? Compute the following.
4) 11P3
5) 8C5
6) What is the major difference between a permutation problem and a combination problem?

Students were told that there would be a quiz the next day, and they could use only their assignment as a resource. The quiz was a group quiz (my classes are made up of groups of 4 students), and there was a "battle" between pairs of groups that sis next to each other. The winners of each battle earned the right to drop 1 homework score for the semester. Here is a copy of the quiz, which I displayed on a screen using PowerPoint.

1.       What color ink did I use to write on the PowerPoint slides?

2.       A class has 40 students. The instructor randomly selects 3 students.
The first wins a $20 gift certificate, the second wins a new calculator, and the third wins a new eraser.
In how many different ways can the instructor choose the 3 students?

3.       Faculty passwords in Banner are made up of 4 digits (0 – 9).
How many different passwords are possible?

4.       The math department has 16 faculty.
In how many different ways can the Dean select 3 instructors to attend a conference?

5.       Compute: 12C5.

6.       Compute: 9P4.

7.       License plates in Rhode Island have 2 letters followed by 3 digits.
Neither letter can be I or O.
No digit can be used more than once.
How many different license plates are possible?

8.       What are the 3 conditions that tell us a problem calls for the use of combinations?

9.       Make up a problem whose solution is 6 x 4 = 24.

10.   Fifteen patients sign up to participate in a trial for a new medication.
In how many different ways can the doctor select 6 of the patients to receive a placebo?

Bonus Question: What was the address of the web site mentioned at the end of the video for students who needed extra help? 

The groups got 1 minute for each of the first 4 problems, and 2 minutes for each of the last 6 problems. The first question was to break the tension, and we had a good laugh when I told them later that the correct answer was "Skittles Red". The bonus question only counted in case of a tie after the first 10 questions.

I was really happy with the results. There was a lot of great discussion within the groups, and I feel that they truly understood what hey were doing. (They went on to do really well on the counting problems on the probability exam.)

- George

If you have questions or comments, please leave a comment on this blog or reach me through the contact page on my website: georgewoodbury.com