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16 Jun 2010, 11:03
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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?
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?
16 Jun 2010, 11:21
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dlwilson1122
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.
16 Jun 2010, 11:25
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thanks for explaining
