There are more reasons, and it goes a lot deeper, than just following this one pattern. The entire binomial theorem relies on 0! being 1, unless you start putting in huge numbers of exceptions and special cases.<p>Here's a better answer: <a href="https://mathforum.org/library/drmath/view/57128.html" rel="nofollow">https://mathforum.org/library/drmath/view/57128.html</a><p>If you prefer video: <a href="https://www.youtube.com/watch?v=Mfk_L4Nx2ZI" rel="nofollow">https://www.youtube.com/watch?v=Mfk_L4Nx2ZI</a>