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6 horses {A,B,C,D,E,F} Participate in a race. If there are no draws in

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Location: India
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6 horses {A,B,C,D,E,F} Participate in a race. If there are no draws in [#permalink]

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New post 28 Sep 2017, 06:16
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Question Stats:

48% (01:36) correct 52% (01:36) wrong based on 44 sessions

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6 horses {A,B,C,D,E,F} Participate in a race. If there are no draws in the rate then in how many ways can the race end such that horse A always finishes ahead of C and B both the horses?

A) 720
B) 360
C) 240
D) 120
E) 48

Source: www.GMATinsight.com
[Reveal] Spoiler: OA

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Re: 6 horses {A,B,C,D,E,F} Participate in a race. If there are no draws in [#permalink]

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New post 28 Sep 2017, 07:12
GMATinsight wrote:
6 horses {A,B,C,D,E,F} Participate in a race. If there are no draws in the rate then in how many ways can the race end such that horse A always finishes ahead of C and B both the horses?

A) 720
B) 360
C) 240
D) 120
E) 48


There are four cases:

#1 Horse A finished first (B and C were put arbitrary):

A _ (B) _ (C) _ = all other houses can be arranged in 5! ways = 120

#2 Horse A finished second (and etc.):

_ A _ (B) _ (C) = 3C1 for the first place and 2C2*4! For the last 4 places = 3*1*24 = 72

#2 third:

_ _ A _ (B) (C) = 3C2 * 3! = 36

And finally A finished fourth:

_ _ _ A (B) (C) = 3C3*3!*2! = 12

Total = 120 + 72 + 36 + 12 = 240

Answer C

Kudos [?]: 1 [0], given: 193

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6 horses {A,B,C,D,E,F} Participate in a race. If there are no draws in [#permalink]

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New post 28 Sep 2017, 10:42
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GMATinsight wrote:
6 horses {A,B,C,D,E,F} Participate in a race. If there are no draws in the rate then in how many ways can the race end such that horse A always finishes ahead of C and B both the horses?

A) 720
B) 360
C) 240
D) 120
E) 48



This reminds me of another problem I've seen where instead of A always finishing infront of both B and C, A always finished infront of Just B.

In this situation there are 6! combinations but 1/2 of the total possibilities include B finishing in front of A. Thus the solution would be 6!/2 = 360

In this case, A finishes in front of both B and C. There are equal possibilities that B finishes in front of A and C, and that C finishes in front of A and B. Thus A will finish in front of BOTH B and C 1/3 of the time.

So the answer logically is 1/3 of the total possibilities.

6! / 3 = 240 which is the correct answer.

Kudos [?]: 5 [1], given: 56

Expert Post
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Joined: 08 Jul 2010
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Re: 6 horses {A,B,C,D,E,F} Participate in a race. If there are no draws in [#permalink]

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New post 30 Sep 2017, 00:05
GMATinsight wrote:
6 horses {A,B,C,D,E,F} Participate in a race. If there are no draws in the rate then in how many ways can the race end such that horse A always finishes ahead of C and B both the horses?

A) 720
B) 360
C) 240
D) 120
E) 48

Source: http://www.GMATinsight.com


METHOD 1:

We need 3 places for A B and C which can be selected in 6C3 ways

Now A has to seated on the first selected place and B and C can exchange position on the remaining two positions in 2! ways

Remaining three individuals can occupy the positions in 3! ways

Total ways of arranging them as desired = 6C3 * 2! * 3! = 20*2*6 = 240


METHOD 2:

A has equal chances of being ahead of B and C as B and C have to be ahead of other two hence

probability of A to be ahead of both B and C = 1/3

Total ways of arranging the six individuals = 6! = 720 ways

Favourable cases = (1/3)*720 = 240

METHOD 3:
If A comes at first place A - - - - - then arrangements = 5!
If A comes at Second place - A - - - - then arrangements = 4C2*2!*3! = 72
If A comes at Third place - - A - - - then arrangements = 3C2*2!*3! = 36
If A comes at Forth place - - - A - - then arrangements = 2C2*2!*3! = 12

Total ways = 120+72+36+12 = 240

Answer: Option C
_________________

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GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2279 [0], given: 51

Re: 6 horses {A,B,C,D,E,F} Participate in a race. If there are no draws in   [#permalink] 30 Sep 2017, 00:05
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