In his lectures about combinatorics, Mr. Davis touched upon various topics. He gave students problems about counting the ways to rearrange and pick items, using candy as a visual to help the students understand. He also talked about the various strategies used to solve these problems. These strategies included using “bars and stars” to represent the problem, and using the Inclusion-Exclusion Principle. Lastly, he demonstrated the numerous applications of the famous Pascal’s Triangle.
Sample Problems:
Say there are 5 Jolly Ranchers and 3 Starbursts. How many ways are there to pick a Jolly Rancher or a Starburst? How many are there to pick a Jolly Rancher and a Starburst?
How many different ways are to rearrange the letters in the word ALABAMA?
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A
How many paths are there from point A to point B only going up and right?
If there are 3 people and 5 different candies, how many ways are there to distribute the candies if each person has to get at least one candy?
