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Bunuel
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Twelve runners enter a race to compete for first, second, and third pl 18 Dec 2019, 03:02
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E
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25% (medium)

Question Stats:

67% (00:46) correct 33% (00:55) wrong based on 141 sessions

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Twelve runners enter a race to compete for first, second, and third place. How many different combinations of winners are possible?

A. 6
B. 220
C. 440
D. 660
E. 1320
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E
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Twelve runners enter a race to compete for first, second, and third pl 19 Dec 2019, 01:30
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In this question, we need to select 3 winners and arrange them in position first, second, and third.
= 12C3*3!
= (12.11.10)/3! * 3!
= 1320

Answer = E

Bunuel
Twelve runners enter a race to compete for first, second, and third place. How many different combinations of winners are possible?

A. 6
B. 220
C. 440
D. 660
E. 1320
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Twelve runners enter a race to compete for first, second, and third pl 19 Dec 2019, 01:48
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I am clear that as we have 12 persons which will be n and 3 positions which will be r
So the total combination gonna be nCr
Could yo u please explain why do we need to multiply with 3!

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Twelve runners enter a race to compete for first, second, and third pl 19 Dec 2019, 02:12
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by 12C3 , we have selected 3 persons A, B, C who will get position 1, 2, 3.
But there can be many arrangement who get which position.
For example,
(1,2,3) position can be ABC or BAC or CBA etc

there will 3! arrangement
hence , 3! is to be multiplied.


SuryaNouliGMAT
I am clear that as we have 12 persons which will be n and 3 positions which will be r
So the total combination gonna be nCr
Could yo u please explain why do we need to multiply with 3!

Posted from my mobile device
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Twelve runners enter a race to compete for first, second, and third pl 19 Dec 2019, 02:21
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Understood..thanks for the clear explanation:-)


gmatbusters
by 12C3 , we have selected 3 persons A, B, C who will get position 1, 2, 3.
But there can be many arrangement who get which position.
For example,
(1,2,3) position can be ABC or BAC or CBA etc

there will 3! arrangement
hence , 3! is to be multiplied.


SuryaNouliGMAT
I am clear that as we have 12 persons which will be n and 3 positions which will be r
So the total combination gonna be nCr
Could yo u please explain why do we need to multiply with 3!

Posted from my mobile device
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Twelve runners enter a race to compete for first, second, and third pl 19 Dec 2019, 10:20
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Bunuel
Twelve runners enter a race to compete for first, second, and third place. How many different combinations of winners are possible?

A. 6
B. 220
C. 440
D. 660
E. 1320
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For first position, number of options = 12
For second position, number of options = 11
For third position, number of options = 10

Total combinations = 12*11*10 = 1320

IMO E

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Twelve runners enter a race to compete for first, second, and third pl 19 Dec 2019, 13:14
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Bunuel
Twelve runners enter a race to compete for first, second, and third place. How many different combinations of winners are possible?

A. 6
B. 220
C. 440
D. 660
E. 1320
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Three runners so 12 for 1st, 11 for 2nd, 10 for third

12*11*10 so result will end in 0. 12*11 > 10*10 so result is > 10*10*10 = 1000. Only 1320 is possible
IMHO
E
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Twelve runners enter a race to compete for first, second, and third pl 26 Dec 2019, 21:14
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Bunuel
Twelve runners enter a race to compete for first, second, and third place. How many different combinations of winners are possible?

A. 6
B. 220
C. 440
D. 660
E. 1320
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Because the order of finishing the race is important, we must use the permutations formula instead of the combinations formula. Thus, we have: 12P3 = 12! / 9! = 12 x 11 x 10 = 1320

Answer: E
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Twelve runners enter a race to compete for first, second, and third pl 31 Jan 2020, 03:16
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gmatbusters
by 12C3 , we have selected 3 persons A, B, C who will get position 1, 2, 3.
But there can be many arrangement who get which position.
For example,
(1,2,3) position can be ABC or BAC or CBA etc

there will 3! arrangement
hence , 3! is to be multiplied.


SuryaNouliGMAT
I am clear that as we have 12 persons which will be n and 3 positions which will be r
So the total combination gonna be nCr
Could yo u please explain why do we need to multiply with 3!

Posted from my mobile device
Show more


As far as I understand it, it is asked for the combination of winners. Thus the order does not matter.
The answer would be 220. Why is this wrong or how should I understand, that the question asks for the arrangement of the winners?
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Twelve runners enter a race to compete for first, second, and third pl 29 Sep 2024, 21:06
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