Introduction to number theory (Berkeley Math 115) - Introduction to number theory lecture 8. Applications of binomial coefficients

This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We discuss some applications of binonial coefficients, such as an approximate estimate for the number of primes less than n, and the Catalan numbers. The textbook is "An introduction to the theory of numbers" by Niven, Zuckerman, and Montgomery (5th edition).