There are 8 candidates for three positions at a restaraunt. one position is for a cook. the second position is for a food server. the third position is for a cashier. if all 8 candidates are equally qualified for the three positions, in how many different ways can the three positions be filled?

You do not have to worry about permutation (counting 2 or more possibilities multiple times) as the positions are unique. 

So you can think of these kind of questions step by step. 
1st step: 
How many ways can you fill the 1st position? (cook)
8 candidates, this 8 ways

2nd step: 
For 8 different cooks how many food servers can be selected?
As a persion cannot be cook and server for any cook selected there are 7 different people who can be servers, so this is 8*7 ways

3rd step: 
For all the 8*7 ways of cooks there are 6 people who can be cashiers. 

So the solution is: 8*7*6=336