Stirling's Approximation is a good estimate for the factorial function. Let's explore a derivation for it.
This is part of a series on combinatorics: https://www.youtube.com/playlist?list=PLH5zdqQODdBjbFarfKUmK1uG6L-DIVcR_
A full proof of Stirling's formula can be found here: https://faculty.washington.edu/moishe/hanoiex/counting/Stirling.pdf
Proofs of Wallis' formula from 3 Blue 1 Brown: https://www.youtube.com/watch?v=8GPy_UMV-08 and Mathologer: https://www.youtube.com/watch?v=WL_Yzbo1ha4
Sections
0:00 Introduction
2:12 Lower and Upper Bounds
4:00 Estimating the Logarithm
7:54 Wallis' Formula
13:02 Recap