Pascal's Triangle But The World Isn't Flat #SoME3

This video took so long to make it makes me feel sad. I&actually so proud of this and it is an idea that which I think is so elegant. I really hope you enjoy the video and if enjoy, be sure to like and subscribe. :D This is my submission for the Summer of Math Exposition, hosted by @3blue1brown Gigantic Credits Go To The Following: Franek1334 - Helped me hugely with the animations in 3D. An incredible teacher and coder who helped a lot. Abulafia - Helped me smooth out the animations and improve the quality of the video. (and save a couple hours) Uwezi - Also helped me with the animations in 3D. Aiyush Gupta - Helped produced the model for the binomial distribution and trinomial distribution and by helped, I mean saved me from torture. Actual Legend. Helped a lot with some major design choices too. Seriously big credit. Animation of the Pentacharon - JasonHise at English Wikipedia, Public domain, via Wikimedia Commons under a CC0 License which I definitely don&know how to code. Timestamps: 0:00 The Game 1:23 Introduction 2:21 Binomial Expansion 6:08 Trinomial Expansion 11:46 Probability Distributions 13:07 Quadnomial Expansion? 16:47 Conclusion