### Home > CCG > Chapter 10 > Lesson 10.3.4 > Problem10-158

10-158.

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

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

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.

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 $_5C_0$?