Combinatorics is a branch of mathematics which is about counting – and we will discover many exciting examples of “things” you can count.  You can use combinatorics to calculate the “total number of possible outcomes”. 

Spark your thinking!

1. Set up your math mini spark recording page: #103: Combinatorics

To do this mini spark you need to know a little about factorials. Steps 2 and 3 will review them for you.

2. The factorial function (symbol: !) says to multiply all whole numbers from our chosen number down to 1. Example: 4! = 4 × 3 × 2 × 1 = 24.

Complete these two problems so that they look similar to the example:

Example: 6! = 6 x 5 x 4 × 3 × 2 × 1 = 720

5! =

9! =

Scroll to the bottom of this post to see if you are correct. If you got it correct, add a star. Add the correct answer if needed.

3. Watch this short video that show you how to divide factorials. Don’t worry. It isn’t hard. Do the problems with the teacher on your recording page.

4. Study the first two columns of this teaching page.  Write the type of the formulas and the formulas on your recording page.

5.  Watch this video. Do the first two math problems with the teacher on your recording page. Try the last problem by yourself on your recording page. The answer is at the end of this post.

 

Advanced: Check out this teaching page. Each of the sections has a mini lesson, a practice problem, and a solution.  Read each lesson and try the problem on your recording page. Check your work. If you complete this, talk with your EY teacher about using this as a badge option.

Factorials

Permutations

Combinations

Combinatorics and Pascal’s Triangle

Combinatorics and Probability

6. Share your math mini spark recording page with your teacher/EY coordinator

 

 

 

 

5! = 5 x 4 × 3 × 2 × 1 = 120

9! = 9 x 8 x 7 x 6 x 5 x 4 × 3 × 2 × 1 = 362,880

 

 

50 people are in a race. How many ways can gold, silver, and bronze be awarded?