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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
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In a 4 person race, medals are awarded to the fastest 3 runners. The
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10 May 2021, 21:48
10 May 2021, 21:48
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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
A. 24
B. 52
C. 96
D. 144
E. 648
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Re: In a 4 person race, medals are awarded to the fastest 3 runners. The
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12 May 2021, 22:30
12 May 2021, 22:30
1
GeminiHeat wrote:
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
A. 24
B. 52
C. 96
D. 144
E. 648
Possible combinations:
GGG = \(^4C_3 = 4\)
GGS = \((^4C_2)(^2C_1) = 12\)
GSS = \((^4C_1)(^3C_2) = 12\)
GSB = \((^4C_1)(^3C_1)(^2C_1) = 24\)
So, a total of 52 victory circles
Hence, option B
Re: In a 4 person race, medals are awarded to the fastest 3 runners. The
[#permalink]
10 Mar 2024, 21:55
10 Mar 2024, 21:55
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