infinitely many people failed this interview question @drpeyam

Uploaded November 2024 | Updated September 2026, 1 week ago

infinitely many people failed this interview question

We calculate infinity bang divided by infinity factorial. In other words, out of all permutations of infinitely many objects, how many are derangements? This is useful for example, for Secret santa, where you want to make sure that no one gets their own gifts, or for making sure that students don't grade their own exam. The answer will surprise you! For this, we use an explicit way of calculating the derangements by using the inclusion-exclusion principle, and finally by using a power series. This is a must-see for calculus and probability and combinatorics students, enjoy!

Derangements: youtu.be/lqB8eiy2X-E

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$Solving the logistic equation Solving the logistic equation. What does the fox say? Here I solve a differential equation using separation of variables and partial fractions and integrals. It models the population of bunnies but with a limited factor. It gives a surprisingly good model approximation of populations like in Belgium. Enjoy this calculus adventure Subscribe to my channel: https://youtube.com/drpeyam TikTok: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$

$Half integral of x Defining the half integral, which is halfway between a function and its integral. Done by analogy with half derivatives, by finding formulas for the derivatives of power functions. It uses the factorial which is then generalized to the gamma function with Gaussian integrals. I also mention trig functions and applications to broken processes. This is a delight for any calculus student or anyone who is interested in fractional derivatives. 0:00 Introduction 0:30 Analogy 2:58 Gamma Function 5:00 Half integral of x 9:37 Properties and Applications Half Derivative: https://youtu.be/gaAhCTDc6oA YT channel: https://youtube.com/drpeyam TikTok channel: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$