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

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

by Vincen » Tue Feb 13, 2018 3:31 am
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. n/2

The OA is the option A.

Experts, what is the formula that I should use here? Can you help me? Thanks in advanced.
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by Scott@TargetTestPrep » Wed Feb 14, 2018 10:18 am
Vincen 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. n/2
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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by [email protected] » Wed Feb 14, 2018 2:44 pm
Hi Vincen,

We're told that there are N cities. We're asked for the number of airlines that connected 2 different cities (and that an airline from city A to city B is DIFFERENT from an airline from city B to city A). This question can be solved by TESTing VALUES.

IF N=2, then there are 2 cities and two 'routes' (A to B and B to A). So we're looking for an answer that equals 2 when N=2. There's only one answer that matches...

Final Answer: A

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