Combinatorics - in how many ways question A store sells shirts, 3 different brands, 5 different sizes, 4 different colors. 
(Sizes and colors are similar to 3 brands, example: all brands have sizes from 1 to 5.)

1) How many ways a customer can buy 3 different shirts?
2) How many ways 3 customers can buy 3 shirts? (one shirt for each)?
3) How many 3 customers can buy 3 different shirts? (one for each)?


Answers: 
1) $C^{60}_3$ 
2) $60^3$
3) $P^{60}_3$
My question is: How can we distinguish which formula to use for each? how can we figure out when is order is important, or if there is a repeating ?
 A: A) note all 3*5*4 shirts are different, so you need to select 3 different out 60. Order doesn't matter, because, roughly speaking, you are only interested in the 'final result', and whether you chose shirt A then shirt B or vice versa doesn't matter, so you divide by the total number of ways to select, i.e. 3!
B) Two different customers can select the same shirt,
C)Once a customer bought a shirt it is removed from the 'stack', and customer 1 buying shirt A is different from customer 2 buyng shirt B is different from customer 1 buyng shirt B and customer 2 buying shirt A.
A: In the first one, the order does not matter because they are all being bought by the same person. All he wants is to go out of the shop with 3 shirts, and he does not care which one he bought first, second or third.
In the second one, the order is again irrelevant, but the choice made by each person is completely independent upon what the others buy. Each person has the choice of one of 60 shirts.
In the third one, the order does matter, because while we are picking 3 shirts out of 60, which person we assign each one to is important. So say we pick 3 shirts. Then there are 3 people to assign each one to, and therefore there are as many ways to assign them as there are ways to order 3 people.
