The best way to solve this problem is to imagine the situation as follows: Suppose that each position (first, second and third) is a numbered box. (first is box number one, and so on).
Now, imagine that each student is a ball that is numbered from 1 up to 11.
The situation translates to calculate in how many different ways we can put a ball in each box, without putting 2 balls in each box. We have the following
To solve this, we will use the multiplication principle. This principle relays on multiplying the number of possibilites for each box. Consider the case in which we will fill the box number 1. We can choose any of the numbers, so we have 11 posibilites. Now, suppose that we chose one number for box 1, and now we want to fill box 2. Then, we will have 10 possibilites only, since we already picked one. In the same manner, to fill the third box we have 9 possibilities. So the total number of possibilites is the product of this three numbers. That is
