Five people are running in a race. The first one to finish

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Five people are running in a race. The first one to finish [#permalink]

13 Mar 2012, 20:15

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Five people are running in a race. The first one to finish wins a gold medal, the second wins a silver medal and the third wins a bronze medal. How many different arrangements of medal winners, in order from first to third, are possible?

A. 5
B. 10
C. 60
D. 120
E. 125

[Reveal] Spoiler: OA

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Re: permutations & Combinations [#permalink]

13 Mar 2012, 20:34

Assuming no ties in the race :

The Gold Medal can be given in 5 ways
The Silver Medal can be given in 4 ways
The Bronze Medal can be given in 3 ways

So total number of ways = 5 * 4 * 3 = 60

Answer - C
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Manager

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Re: permutations & Combinations [#permalink]

13 Mar 2012, 21:14

same type of question where order doesn't matter

Five people are running in a race. The first three to finish win
gift certificates. How many different groups of people could
win the gift certificates?
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Re: permutations & Combinations [#permalink]

13 Mar 2012, 21:19

Here it's 5C3 = 5!/3!2!
= 5*4/2 = 10

The idea is to pick a group of 3 people out of 5.
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Re: Five people are running in a race. The first one to finish [#permalink]

22 Mar 2012, 09:31

hey all,
whats the answer?

i got it as 60 . is that wrong ?
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Re: Five people are running in a race. The first one to finish [#permalink]

23 Mar 2012, 02:08

pappueshwar wrote:

hey all,
whats the answer?

i got it as 60 . is that wrong ?

OA is given under the spoiler in the initial post.

Five people are running in a race. The first one to finish wins a gold medal, the second wins a silver medal and the third wins a bronze medal. How many different arrangements of medal winners, in order from first to third, are possible?
A. 5
B. 10
C. 60
D. 120
E. 125

C^3_5*3!=60, where C^3_5 is ways to select the group of 3 winners out of 5 contestants and 3! is ways to arranging them (alternately you can just do P^3_5=60).

Answer: C.

Hope it helps.
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Re: Five people are running in a race. The first one to finish [#permalink] 23 Mar 2012, 02:08

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Five people are running in a race. The first one to finish

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Five people are running in a race. The first one to finish

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