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Register now and save up to $200 Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code ## 6 horses {A,B,C,D,E,F} Participate in a race. If there are n tagged by: rolandprowess This topic has 1 expert reply and 1 member reply ### Top Member GMATinsight Legendary Member Joined 10 May 2014 Posted: 998 messages Followed by: 21 members Thanked: 203 times #### 6 horses {A,B,C,D,E,F} Participate in a race. If there are n Thu Sep 28, 2017 5:27 am Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) 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 Answer: Option C _________________ Prosper!!! Bhoopendra Singh & Sushma Jha "GMATinsight" Contact Us Testimonials To register for One-on-One FREE ONLINE DEMO Class Call/e-mail e-mail: info@GMATinsight.com Mobile: +91-9999687183 / +91-9891333772 Get in touch for SKYPE-Based Interactive Private Tutoring One-On-One Classes fee - US$40 per hour &
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### Top Member

regor60 Master | Next Rank: 500 Posts
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Thu Sep 28, 2017 7:11 am
A finishes 1st: 5 options for B x 4 options C x 3 x 2 options for D,E,F = 120
2nd: 4....3...." = 72
3rd: 3.....2..." = 36
4th: 2........." = 12

Total 240 C

### GMAT/MBA Expert

EconomistGMATTutor GMAT Instructor
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Tue Oct 10, 2017 5:27 am
Hello GMATinsight and Regor.

I would like to give you a more detailed solution.

We have 6 horses and we can have the following cases:

- Horse A finishes 1st: here, we have to organize 5 horses in 5 places, the number of ways to do that is A*5*4*3*2*1=5!=120.

- Horse A finishes 2nd: First, we have to pick the horse for the first place but we can not select horses B or C. So, we have 3 options for the first place (D, E, F) and the number of ways to select a horse for the first place is 3. Then we have to organize 4 horses in the last 4 places. The total number of ways in this case is 3*A*4*3*2*1=72.

- Horse A finishes 3rd: as in the case before, we have to pick 2 horses for the first 2 places but we can not select horses B or C. So, we have 3 options again and we can organize this 2 horses in 3*2=6 different ways. Now we have to organize the last 3 horses in the last 3 places. The total number of ways in this case is 3*2*A*3*2*1=36.

- Horse A finishes 4th: Now, we have to pick 3 horses for the first 3 places but we can not select horses B or C, the number of ways to organize this 3 horses is 3*2*1=6. Finally, we have to organize 2 horses (B and C) in the last 2 places. The total number of ways in this case is 3*2*1*A*2*1=12.

You should noticed that A can not finish in the 5th place or in the 6th place.

In conclusion, the total number of ways this race can end is 120+72+36+12=240.

So, the correct answer is C.

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