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suslik
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Carmelo and LeBron participate in a seven-person footrace. 28 Aug 2005, 17:34
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Carmelo and LeBron participate in a seven-person footrace. If all seven contestants finish and there are no ties, how many different arrengements of finishes are there in which Carmelo defeats LeBron?

A. 5040
B. 2520
C. 720
D. 120
E. 42



Guys, how much time do you need to solve this problem? Any shortcuts?



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Decibel
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Carmelo and LeBron participate in a seven-person footrace. 28 Aug 2005, 18:12
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i got 21 which is not in asnwer. 7!/(2!*5!).
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yaron
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Carmelo and LeBron participate in a seven-person footrace. 29 Aug 2005, 02:12
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It took me some time, but logically:

Total number of arrangements: 7!
For Carmelo and LeBron there are always 2 arrangements where they share opposite places.
For example: xxCxxLx, and xxLxxCx
Since we only want the cases where Carmelo defeats LeBron: 7! / 2 = 2520
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Carmelo and LeBron participate in a seven-person footrace. 29 Aug 2005, 02:13
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Total possible arrangements = 5040

My intuition tells me that in half the cases C will outrun L. So the answer is 5040/2=2520.

Consider that C and L on their own can finish in a total of P(7,2)=6*7=42 arrangements. It's pretty obvious that C will be the winner in half of those cases.
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Carmelo and LeBron participate in a seven-person footrace. 29 Aug 2005, 13:48
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i use POE on these

there are total 7 people including L and J

lets treat L and J as one.

so there are 6 people racing in which C always beats L.

So total combinations with 6 are 720.

total with 7 are 5040.

hence it is a number in between 720 and 5040, which is B...
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Carmelo and LeBron participate in a seven-person footrace. 29 Aug 2005, 15:23
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got it. misread question. 21 would how many ways can C beat L.C(7,2)

answer then would be 21*5!(since there are 5 places left for the remaining contestants) = 2520
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Carmelo and LeBron participate in a seven-person footrace. 29 Aug 2005, 16:17
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OA is 2520.

thanks everybody for the explanations



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Hi there,
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