Overview
On this page, we start discussing the field of Combinatorics, by considering the fundamental counting principle and counting permutations and linear arrangements.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
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Understand the fundamental counting principle that describes how to count the number of possible results when two choices are made in sequence, or when only one of the two is made.
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Understand the meaning of the factorial of a positive integer \(n\).
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
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Be able to count the number of ways of arranging objects in a line when the objects are distinguishable and solve related counting problems using permutations.
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Be able to count the number of ways of arranging objects in a line when some objects are indistinguishable and solve related counting problems using the MISSISSIPPI formula.
To prepare for class
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Watch the following video (by Kolumath) which explains the fundamental counting principle and counting permutations:
After class
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Watch the following videos (by patrickJMT) which explain and show examples of the MISSISSIPPI formula to count linear arrangements with several types of indistinguishable objects:
