Hundreds of Combinatorics Video Lectures

If you are taking mathematics courses related to combinatorics or probability, I found a page from UCLA containing hundreds of video lectures on the said subjects. It is a collection of lectures from 1993 up to the present and includes lectures from famous mathematicians such as Terence Tao.

For more free video lectures, visit the All for Free page of Math and Multimedia. It also contains posts which links to hundreds of free ebooks and software.

Counting the Number of Subsets in a Set

Problem: How many groups can be formed from 5 persons?

The Power Rangers

First, we represent the persons by small letters a, b, c, d, and e, and we denote a group whose members are c and d as {c, d}. We can have a group with 2 members, 3 members, 4 members, and 5 members.  The members in each group are listed below.  » Read more

Understanding the Multiplication Principle

Amanda went shopping and bought three blouses (red, yellow, violet) and 2 skirts (blue,  green) as treat for herself for her birthday. The first thing she did when she got home was tried on the skirts and blouses. Question: In how many ways can she wear them?

Skirt and Multiplication Principle

This problem can be easily answered by pairing each blouse to the two skirts. The red blouse can be paired with the blue or the green skirt. This is also similar to the yellow and violet blouses.

The pairing above can also be represented using a tree diagram as shown below. For each blouse, we can pair 2 skirts. Since there are three blouses, there are 3(2) = 6 possible ways to wear them. » Read more

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