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# Medals

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Manager
Joined: 29 May 2008
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17 Jun 2009, 05:23
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Five contestants representing five different countries advance ti the final of a fencing championship. All thins being equal, how many possibilities are there with respect to how a first place and a second medal can be awarded?

A) 25
B) 20
C) 45
D) 100
E) 120
Current Student
Joined: 03 Aug 2006
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Schools: Haas School of Business
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17 Jun 2009, 19:23
The answer is B

Direct Solution:
$$5 \times 4 = 20$$

Simplified solution:
First find the number of ways the first place can be won. As there are 5 finalists, there are exactly 5 possibilities for the first place.

Next, the number of ways second place can be won for each first place winner is exactly 4 as a finalist cannot be in both first and second place.

$$\Rightarrow$$ the first and second places can be chosen in $$5 \times 4$$or $$20$$ different ways.
Manager
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18 Jun 2009, 06:36
Use permutation because order matters.

5P2 = 5!/3! = 5*4 = 20
Manager
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19 Jun 2009, 06:02
It was an easy problem, you know that night when I was doing the problems I made so many that it was hard for me to distinguish how simple this problem was, thanks a lot
Re: Medals   [#permalink] 19 Jun 2009, 06:02
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# Medals

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