There are ten lockers in the hallway at school. three new students are to be given lockers. how many different ways could the locker be assigned

 720 you would do 10 x 9 x 8 because the first one can have any of the 10 then it decreases afterwards

Let's first start with the first student. He/she has 10 different lockers to choose from. Because there are 10 lockers. Then second student. He/she has 9 lockers to choose from. Why? Well, the first student picked 1 locker. So, there is one less locker to choose from for the next student. Now all the student picked their lockers. But we want to know how many different ways the lockers could have been assigned. 

The first student had 10 lockers to choose from, right? 
And the second student had 9 lockers to choose from.

So, 10 * 9. Now do that for every student and you get 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1. Multiply the final answer and you get 3628800. Another way to say what we did is we did a factorial. In this case 10 factorial or 10! Also, some people call is shriek or bang.

The exclamation mark means factorial.

No a triangle cannot be formed because when you add the two smallest number together (which would be 11) the have to be bigger than the number it is "against" ( which would be 12)