In how many different ways can the top eight new indie bands be ranked on a top eight list? The top hit song for each of the eight bands will compete to receive monetary awards of $1000, $500 and $250, respectively. In how many ways can the awards be given out?

Question

I think the first question is 8 different ways because they will be ranked on a list of 8.
I think the second question is 8*8*8=512 ways the awards can be given out.....but im not sure if i did this right, please help!

Answer 1

say we have 8 bands numbered 1 through 8
chance that band 1 is top = 1/8
then chance that band 2 is second = 1/7
then chance that band 3 is third = 1/6
etc
so I claim
8! ways (big number, you compute :)

Now how many permutations of 8 taken 3 at a time (permutations not combinations because the order of prizes counts within each group of three) ?

n!/(n-r)! = 8!/(8-3)! = 8!/5! = 8*7*6
= 336

Answer 2

oh okay i get it...