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There are n cities. What is the number of airlines that connected 2 di

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MathRevolution
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There are n cities. What is the number of airlines that connected 2 di [#permalink] New post   02 May 2016, 23:26
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45% (medium)

Question Stats:

62% (01:26) correct 38% (01:20) wrong based on 124 sessions
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There are n cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?

A. n(n-1)
B. n(n+1)
C. n(n-1)/2
D. n(n+1)/2
E. n2

* A solution will be posted in two days.
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A
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chetan2u
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Re: There are n cities. What is the number of airlines that connected 2 di [#permalink] New post   02 May 2016, 23:53
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MathRevolution wrote:
There are n cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?

A. n(n-1)
B. n(n+1)
C. n(n-1)/2
D. n(n+1)/2
E. n2

* A solution will be posted in two days.


Hi,
the Q basically asks to choose two cities out of n and since the DIRECTION is important, we are looking at Permutations or combinations with Order..
\(nP2 = nC2 *2! = \frac{n(n-1)}{2}* 2 = n(n-1)\)
A
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Re: There are n cities. What is the number of airlines that connected 2 di [#permalink] New post   07 May 2016, 08:14
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First of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-1). Hence, the answer is n(n-1), which makes A an answer choice.
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Re: There are n cities. What is the number of airlines that connected 2 di [#permalink] New post   07 May 2016, 12:06
This was not hard as you often put up MATH REVOLUTION
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Re: There are n cities. What is the number of airlines that connected 2 di [#permalink] New post   14 Feb 2018, 11:02
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MathRevolution wrote:
There are n cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?

A. n(n-1)
B. n(n+1)
C. n(n-1)/2
D. n(n+1)/2
E. n2


If airline from city A to city B is same as airline from city B to city A, then we would have nC2 number of airlines. However, since they are different, we have to multiply nC2 by 2. So we have:

nC2 x 2 = n(n - 1)/2 x 2 = n(n - 1) number of airlines

Answer: A
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Re: There are n cities. What is the number of airlines that connected 2 di [#permalink]
14 Feb 2018, 11:02
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