Does order matter when drawing balls from a bag? I have a question. Let's say we draw 5 balls from a bag. This bag has 20 balls. And each ball is numbered from 1 to 20. 
Case 1: The balls are drawn one at a time without replacement. Does order matter? Is 1,2,3,4,5 the same as drawing 5,4,3,2,1? Why/Why not?
Case 2: The balls are drawn all at once without replacement. Is 1,2,3,4,5 the same as 5,4,3,2,1? Does order matter? Why/Why not?
Case 3: The balls are drawn one at a time with replacement. Is 1,2,3,4,5 the same as 5,4,3,2,1? Does order matter? Why/why not?
This is an example mentioned in Mathematics:A Discrete Introduction by Scheinerman. I am confused because I don't understand why the author states his intuitions the way he does. 
 A: Case 1: Order matters and event (1,2,3,4,5)  is not the same as (5,4,3,2,1). Its probability is $\frac{15!}{20!}$. However quite often questions are asked that can also be answered if the order does not matter. On the other hand in many situations it might be handsome to built in some order. If you do that then one thing is for certain: you loose no essential data. It could happen though that things are made more complex than needed.
Advice: start with a model where order does not matter and if you fail to find the answer at first hand then build in some order and try again.
Case 2: Order does not matter and event (1,2,3,4,5)  is the same as (5,4,3,2,1). This because there is no way to distinguish the samples. Its probability is $\binom{20}5^{-1}$.
Case 3: Order matters just as it did in case 1.
A: Adding to @drhab 's answer. 
Whether order matters depends on the context in which the experiment happens as much as on the experimental procedure. For example, if you are picking five people from among $20$ to form a team, the result is the same in your first scenario, even if you announce the team members one at a time as you draw their numbers.
The fact that order matters in the first scenario is implicit in the "one at a time" rather than "all at once". In practical problems (or problems that count as practical from your course in discrete mathematics) what's most important is understanding the problem, not trying to guess the formula to use.
