Seven flute players are listed in the program in random order. How many different ways can the names be listed?

Assuming they all have different names 7! 
(counting principle) 


Take a look: 
7 ways to list first name
6 ways for the second
5 for the third
4 the fourth
3 fifth
2 sixth
1 last 
the total number of ways is the product: 
(7)(6)(5)(4)(3)(2)(1)=7! 

:)