precalculus 12 permutations and combinations
Specific Curriculum Outcomes
PC01 Apply the fundamental counting principle to solve problems.
PC02 Determine the number of permutations of n elements taken r at a time to solve problems.
PC03 Determine the number of combinations of n different elements taken r at a time to solve problems.
PC04 Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).
PC01 Apply the fundamental counting principle to solve problems.
PC02 Determine the number of permutations of n elements taken r at a time to solve problems.
PC03 Determine the number of combinations of n different elements taken r at a time to solve problems.
PC04 Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).
activities
 The Working Principal of the Enigma  The Enigma Machine was a powerful cyrptographic machine used extensively during WWII. Show students how the machine works and let them figure out how many possible ways there are to set up the machine using the fundamental counting principal.
 The Door Lock from Dan Meyer  Given an image of a keypad lock, students brainstorm how many possible combinations a lock might have. What characteristics make for a good lock? There is a link to an additional interesting conversation about information leakage.
 Zero Factorial video from Numberphile  A video that explains why zero factorial is equal to 1.

 Rectangles with Consecutive Integer Sides  Create a set of five rectangles that have sides of length 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 units. You can combine sides in a variety of ways: for example, you could create set of rectangles with dimensions 1 x 3, 2 x 4, 5 x 7, 6 x 8 and 9 x 10. How many different sets of five rectangles are possible? What are the maximum and minimum values for the total areas of the five rectangles?