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

Question

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

Show Answer

Official Answer

C

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

subhashghosh · Answer

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

iwillcrackgmat · Answer

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?

subhashghosh · Answer

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

The idea is to pick a group of 3 people out of 5.

pappueshwar · Answer

hey all,
whats the answer?

i got it as 60 . is that wrong ?

Bunuel · Answer

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.

SaraLotfy · Answer

Hello Bunuel,

I didn't understand why you used  P^3_5=60  to solve this question. Also, the actual evaluation of it seems to get me - I know this is a silly point but I still get it wrong -

I evaluate as follows:

P^3_5 = 5!/3! = 5*4*3*2*1/ 3*2*1 = 20. where am I going wrong?

Bunuel · Answer

First of all  P^n_k=\frac{n!}{(n-k)!} , thus  P^3_5=5!/(5-3)!=60 .

Next, consider the runners to be A, B, C, D and E.

P^3_5  gives all different  ordered  triplets from 5:
ABC
ACB
BAC
BCA
CAB
CBA

ABD
ADB
BAD
BDA
DAB
DBA
...

Hope it helps.

bumpbot · Answer

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

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