This question is probably very baffling to several students. Many students will exclaim $0!=0$ to me, but this is incorrect. To understand why $0!=1$, we need to first look at what $n!$ means; $n!$ is the number of ways to arrange $n$ objects in a row. And we all know that $n!=1 \times 2 \times 3 \ ... \times n$. So shouldn’t $0!=0$?

Think about this, the number of ways to arrange 1 object is 1, that is, put the object there by itself. However, the number of ways to arrange $0$ object is one! Cos there is nothing to arrange so we still have one way to do it.

Give it some thought and feel free to discuss with me!

Related video by Dr James Grime