dlwilson1122 wrote:

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

thanks

Welcome to Gmat Club! Below is the solution for your problem

In how many different ways can the top eight new indie bands be ranked on a top eight list?# of permutations of \(n\) distinct objects is \(n!\), so the answer is \(8!\).

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?# of ways to choose \(n\) objects from \(k\) distinct opbjects when order matters is \(P^n_k=\frac{k!}{(k-n)!}\).

So for our original question as there will be 4 awards, then # of ways to choose 4 bands out of 8, when the order matters is \(P^4_8=5*6*7*8\).

For more on this issue please check Combinatorics chapter of Math Book (link in my signature).

Hope it helps.

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