How do you tell a permutation problem from a combination problem?

Question

Given the questions:

1. How many different groups of 4 students can be made from a class of 40?

and

2. How many different lists of 4 students can be made from a class of 40?

How do you determine which requires a permutation and which requires a combination?

Answer 1

The key is finding out if the order of items are important or not. If the order does matter, it will be permutation, otherwise it is combination. 

In these two examples, we should think about context of the words "Groups" and "Lists". For Groups, the order is NOT important, but because Lists comes with the  index, and the order does matter. So, the first question is combination and the second one is permutation.

Combination:

1. How many different groups of 4 students can be made from a class of 40?

Answer:  $C(40,4) = \binom{40}{4} = \frac{40!}{4!(40-4)!} $

Permutation: 

2. How many different lists of 4 students can be made from a class of 40?

Answer:  $P(40,4)  = \frac{40!}{(40-4)!} $