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Victory Circles

Expert replies
by cypherskull » Fri Aug 24, 2012 11:06 am
In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible?

a) 24
b) 52
c) 96
d) 144
e) 648

OA: B
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Source: — Problem Solving |

by vk_vinayak » Fri Aug 24, 2012 11:56 am
What is a "victory circle". If the 3 winners make a circle, how can it be greater than (3-1)! ?
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by Jim@StratusPrep » Fri Aug 24, 2012 12:04 pm
This question has a lot of issues with it and is not representative of something you would see on the exam:


Tie for Gold

(4x3)/2 x 2 = 12


Tie for Silver

(4) x (3 x 2)/2 = 12

No tie

4 x 3 x 2 = 24

Total here is 48, not sure where the additional 4 would come from because there the fact that people have different medals would mean all the circles are different for the last group and the first two are ultimately combinations of the tied position.

I would say 48, but not sure with this question (aka you won't see this on the exam).
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