Here is another way to think about the question: “What is $0! ?$”

1. How many ways are there to choose all five items from a group of five items? What happens when you substitute into the factorial formula to compute $_5C_5?$ Since you know (logically) what the result has to be, use this to explain what $0!$ must be equal to.

   Hint (a):

   $_nC_r=\frac{n!}{r!(n-r!)}$

2. On the other hand, how many ways are there to choose nothing from a group of five items? And what happens when you try to use the factorial formula to compute $_5C_0?$

   Hint (b):

   See part (a).