Combinatorial Objects: Permutations and Subsets [Discrete Math Class]

This video is not like my normal uploads. This is a supplemental video from one of my courses that I made in case students had to quarantine. This is a follow up to previous a video introducing the Sum Principle and Product Principle four counting. We explore the objects called k-permutations and k-subsets of an n-set. Along the way, we find formulas for counting these objects and investigate other combinatorial interpretations of these objects (like nonattacking arrangements of rooks on rectangular chessboards and NE lattice paths on the integer grid.

Note that this video is part of a series kept in a playlist called [Discrete Math Class]:

If you like this video, please consider subscribing to my channel and let me know in the comments if you'd like to see more like this.

This textbook for the course is the open-source textbook by Oscar Levin:

0:00 : Combinations vs. Permutations
00:11 : Introduction: selecting an ordered list of people from a community.
00:37 : k-permutations
02:39 : Counting with Permutations
04:01 : k-subsets
06:13 : Counting with Subsets
08:51 : Combining Permutations and Subsets

#combinatorics #counting #countingprinciples #sumprinciple #productprinciple #additionprinciple #multiplicationprinciple #combinatorialobjects #permutations #subsets #latticepaths #math #manim #discretemathematics #rooks #chessboard #venndiagrams #nonattackingrooks

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[MiguelRaggi]

Wow, this is awesome. How can you produce so much content? It takes me hundreds of hours to make a video in manim.