Count the Cases: Combinations, Pigeonhole, Monty Hall & Stars and Bars | The Curve Ep 5

Exam 2, and Anika's brain keeps leaving the building. Professor Hale teaches the product rule, why choosing 2 co-captains isn't 5 × 4, the pigeonhole principle, the birthday problem and Monty Hall. The group counts their way out of Marisol's shift conflict, splits Yusuf's 10 mana'eesh 1,001 ways, and proves two of any 5 points in a square are close — then parents' weekend. Episode 5 of 6 of THE CURVE — a free animated EECS 203 Discrete Math course from Bot That Lyfe. An original story set at the University of Michigan — not affiliated with or endorsed by the University of Michigan; the professor and students are fictional. Count the choices one step at a time, multiply, and divide out the orders that don't matter. In this episode: • The product rule (outfits, passwords) • Order matters vs. doesn't (permutations vs. combinations) • The pigeonhole principle and the birthday problem • Monty Hall and stars and bars 📘 Free workbook + homework + answer key (PDF): https://botthatlyfe.com/courses/the-c... ▶ Watch the whole season in order:    • The Curve — Learn Discrete Math & Proofs (...   CHAPTERS 0:00 Cold open: the stairwell 0:23 The product rule 0:55 Spot the lie: order 1:23 Pigeonhole 1:54 Monty Hall 2:29 Eight ways 3:00 1,001 mana'eesh 3:49 Five points 4:28 Exam 2 4:50 61% 5:10 Parents' weekend 5:32 Re: Discord THE SEASON 1. Knights and Knaves —    • Half of You Will Fail: Logic, Truth Tables...   2. Proof by Contradiction —    • $200 for the Exam Answers? How to Write a ...   3. Some Infinities Are Bigger —    • Some Infinities Are Bigger Than Others: Se...   4. The Next Step —    • I Got a 41 — How Induction Actually Works ...   5. Count Me In ← you are here 6. The Curve —    • The Curve Was Never the Test: Graphs, the ...   Next: Ep 6 · The Curve —    • The Curve Was Never the Test: Graphs, the ...   Sources & further reading: • Rosen, K. H. Discrete Mathematics and Its Applications, §6.1–6.5 (counting, pigeonhole, permutations and combinations, distributions) • Selvin, S. (1975). A problem in probability (the Monty Hall problem). The American Statistician 29(1). Bot That Lyfe — a free animated CS series every week: https://botthatlyfe.com · courses + workbooks: https://botthatlyfe.com/courses Studio audience laughter: "approx 800 laughter" by lonemonk (freesound.org), CC BY 3.0. #DiscreteMath #Proofs #ComputerScience