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# In a 4 person race, medals are awarded to the fastest 3 runn

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Math Expert
Joined: 02 Sep 2009
Posts: 46166
Re: In a 4 person race, medals are awarded to the fastest 3 runn [#permalink]

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05 May 2017, 09:57
IIMC wrote:
One of the key things mentioned here is " they stand in a victory circle" so shouldn't we multiple 52 with 2!, for making an appropriate circle arrangement in each case.

This is addressed above: victory circle is not the actual circle. Question asks how many different scenarios are possible for: medal-person; medal-person; medal-person.
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Concentration: General Management, Entrepreneurship
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Re: In a 4 person race, medals are awarded to the fastest 3 runn [#permalink]

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10 Sep 2017, 08:01
Bunuel wrote:
kirankp 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

Possible scenarios are:

1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;
2. Gold/Gold/Silver/No medal - 4!/2!=12;
3. Gold/Silver/Silver/No medal - 4!/2!=12;
4. Gold/Gold/Gold/No medal - 4!/3!=4.

Total: 24+12+12+4=52

fantastic explanation i missed the all Golds circle
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Manager
Joined: 21 Jun 2015
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Re: In a 4 person race, medals are awarded to the fastest 3 runn [#permalink]

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10 Sep 2017, 11:17
GGGN+GGSN+GSSN+GSBN=4P3+4P2+4P2+4P1=24+12+12+4=52 hence B
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Joined: 04 Feb 2017
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Re: In a 4 person race, medals are awarded to the fastest 3 runn [#permalink]

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10 Sep 2017, 11:35
Bunuel wrote:
kirankp 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

Possible scenarios are:

1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;
2. Gold/Gold/Silver/No medal - 4!/2!=12;
3. Gold/Silver/Silver/No medal - 4!/2!=12;
4. Gold/Gold/Gold/No medal - 4!/3!=4.

Total: 24+12+12+4=52

Arent we talking about Circular Permutation?
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In a 4 person race, medals are awarded to the fastest 3 runn [#permalink]

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10 Sep 2017, 14:26
4p3
4C2 * 2C1
4C1 * 3C2
4C1

=> B

the alternative solution is to check all options.
sincere the gap between 2 options is too wide, and the right answer must have greater value than 24 => b
In a 4 person race, medals are awarded to the fastest 3 runn   [#permalink] 10 Sep 2017, 14:26

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