There are 10 sprinters competing for first, second, and third place ribbons. How many different ways can the ribbons be awarded?

720

360

72

30

In this case, you can use permutation to answer the question. Permutation is " All possible arrangements of a collection of things, where the order is important." This means that if you have 1,2,3 and 4, and you need to choose 2 from these numbers, the possible outcomes are (1,2), (1,3), (1,4), (2,1) (2,3) etc.

We use nPr for permutation, where n is the number of choices you can pick from. In this case, there are 10 people, so n is 10. r is the number of people you have to pick. Since there are 3 places, r is 3. If you have a scientific calculator, you can type 10P3. If not you can do it manually. using the equation n! / (n-r) !. An example of how to use!, 5!=5*4*3*2*1

now just plug in n and r into the equation.

10! / (10-3) !

=10!/7!

=720

So the answer is 720

720

10! / (10-3) !

10!/7!

10*9*8