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Eight athletes compete in a race in which a gold, a silver and a bronz

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Eight athletes compete in a race in which a gold, a silver and a bronz [#permalink] New post   28 Feb 2023, 10:53
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Eight athletes compete in a race in which a gold, a silver and a bronze medal will be awarded to the top three finishers, in that order.

Quantity A
Quantity B
The number of ways in which the medals can be awarded
8 * 3!



A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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A
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Mohammzk
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Re: Eight athletes compete in a race in which a gold, a silver and a bronz [#permalink] New post   24 Mar 2023, 12:27
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so here we are concerned about the positions with gold, silver and bronze. So we have to use the permutation formulae.
A -> 8P3 = 56 ways
B -> 8! = 48 ways
so quantity A is greater than quantity B
Also a quick note; the nPr = n!/r!(n-r)!
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Re: Eight athletes compete in a race in which a gold, a silver and a bronz [#permalink] New post   17 Sep 2023, 23:13
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The number of ways in which the gold, silver, and bronze medals can be awarded among eight athletes is 336. This is a permutation problem, where order matters. The calculation is as follows:
The gold medal can be awarded to any of the 8 athletes, so there are 8 possibilities. Once the gold medal has been awarded, there are 7 athletes left for the silver medal. Finally, there are 6 athletes left for the bronze medal. So, the total number of ways is 8∗7∗6=336

So A>B
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Re: Eight athletes compete in a race in which a gold, a silver and a bronz [#permalink] New post   03 Oct 2023, 07:25
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A= 8C1*7C1*6C1 = 8*7*6

Hence, A>B
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Re: Eight athletes compete in a race in which a gold, a silver and a bronz [#permalink]
03 Oct 2023, 07:25
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