Probability

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derotts3

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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, $250, and $100; respectively. In how many ways can the awards be given out?

would you multiply the prizes to determine how many ways?

this is confusing to me - thanks for any help / explanation
 
derotts3 said:
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, $250, and $100; respectively. In how many ways can the awards be given out?

would you multiply the prizes to determine how many ways?

this is confusing to me - thanks for any help / explanation
Click to expand...

You can rank n items into n slots in n! ways
 
On first place you can set 10 bands, on second – 9 (because one of bands is already on first place), on third – 8 (because one band on first place and another on second) … on tenth only 1.
Using rule of product we have: 10*9*8*7*6*5*4*3*2*1=10! = 3 628 800 ways

You need to use Ak/n=n!/(n-k!)
 
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