Answer:
120 ways
Step-by-step explanation:
Alice, Bob, David, Charlie,   Eve 
David, Alice, Bob,  Charlie,   Eve 
 Alice,David, Bob,  Charlie,   Eve 
Charlie,   Eve ,Alice,David, Bob,  
Charlie,   Eve ,Alice, Bob, David,
Charlie,   Eve ,David, Alice, Bob,
Alice,Charlie,   Eve , Bob, David, 
Alice,Charlie,   Eve ,  David, Bob,
Bob,Alice,Charlie,   Eve ,  David,   and so .
This is a permutation question as the order of placing Charlie to the left of Eve is important.
So the total number of people n= 5 and the possible order is 4 keeping Charlie left of Eve. Eve cannot have the last position to keep Charlie on the left.
Using the formula of nPr = n!/ (n-r)! we get 
5! / (5-4)! = 120 ways in which Charlie can be placed to the left of Eve.