Question

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

Answer 1

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

Answer 2

720

10! /(10-3)!
10!/7!
10*9*8