Carmelo and LeBron participate in a seven-person footrace on the baske

Question

Carmelo and LeBron participate in a seven-person footrace on the basketball court during All-Star Weekend. If all seven contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?

(A) 5040
(B) 2520
(C) 720
(D) 120
(E) 42

Kudos for a correct solution.

(A) 5040
(B) 2520
(C) 720
(D) 120
(E) 42

peachfuzz · Answer

7! = 5040
5040/2=2520 half the time carmelo is in front, vice versa

Answer:
(B) 2520

D3N0 · Answer

Ans: B
Solution: arranging 7 person on 7 position where specific one person is always ahead of the other specific = 7!/2 = 2520

Bunuel · Answer

PRINCETON REVIEW OFFICIAL SOLUTION:

Carmelo beats LeBron? Carmelo beats LeBron? No one said anything about specific results, especially not on a question that includes so many people.

Many questions on the GMAT can be overwhelming in appearance so first thing…Relax. This question looks nasty, but it’s pretty straightforward, requiring two things: the basic first calculation and then some additional work to solve the problem. It would be extremely painful to try to calculate this whole question in one fell swoop. So don’t.

Calculate out all possibilities first to get your bearings. That is, how many different arrangements, period? Since the order of arrangement again matters, this is another permutation. And since we’re placing all seven runners, this calculation is…

7 x 6 x 5 x 4 x 3 x 2 x 1, cash and prizes worth 5040 arrangements.

Now, what to do? Again, some nice deep breathing to control your nerves – relax and think. These 5040 arrangements are a comprehensive list; every possible seven-person order of finish has been counted. So, we have accounted for every time Carmelo beats LeBron AND every time LeBron beats Carmelo. Doesn’t it make sense that, for every time Carmelo beats LeBron, there is exactly one other instance in which LeBron beats Carmelo? Or more simply, doesn’t it make sense that, if these 5040 represents everything, that Carmelo beats LeBron exactly 50% of the time and vice versa?

The thought takes time. You need to have the presence to recognize that grinding your way in, around, and through this question could take roughly forever. Stepping back and recognizing that this is simply a 50/50 proposition and applying that thought to the 5040 you cranked out gives you 2520. The answer is B.

A consistent approach to certain question types can play a major role in earning more points as you build your analytic and math skills as well as your confidence. Coaches in basketball can improve your game just like a GMAT coach can do the same.

Bunuel · Answer

Similar questions to practice: 7-people-a-b-c-d-e-f-and-g-go-to-a-movie-and-sit-180985.html mother-mary-comes-to-me-86407.html (or: mary-and-joe-126407.html); six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-the-126151.html in-how-many-different-ways-can-the-letters-a-a-b-91460.html goldenrod-and-no-hope-are-in-a-horse-race-with-6-contestants-82214.html meg-and-bob-are-among-the-5-participants-in-a-cycling-race-58095.html over-the-course-of-a-full-day-seminar-66-students-must-give-short-pre-192852.html Check other Arrangements in a Row and around a Table questions in our Special Questions Directory .

chesstitans · Answer

the question leaves me stunned with its ambiguous words. I hardly catch the idea that there are 7 runners in a race. I just bother "tie" or "basketball".

igtroy123123 · Answer

for real : Lebron wins always (whatever may be the situation, just don't put him against MJ ) , For Question Purpose , thank you for the amazing answer

rsrighosh · Answer

If all seven contestants finish  (including Charles Barkley)

what is the intention behind adding the highlighted part in the question.

igtroy123123 · Answer

You gotta give Chuckster his Space there, its a law of nature

Posted from my mobile device

Kinshook · Answer

Given: Carmelo and LeBron participate in a seven-person footrace on the basketball court during All-Star Weekend. 
Asked: If all seven contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?

Number of different arrangements of finishes are there in which Carmelo defeats LeBron = 7!/2 = 2520
Since there are total 7! ways to arrange the results and in half of them Carmelo defeats LeBron.

IMO B

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Carmelo and LeBron participate in a seven-person footrace on the baske

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