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

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by Max@Math Revolution » Mon May 02, 2016 10:45 pm
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

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by Max@Math Revolution » Sat May 07, 2016 7:11 am
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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by 800_or_bust » Sat May 07, 2016 11:22 am
Max@Math Revolution 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.
Approaching this conceptually, each individual city would have an airline to (n-1) cities (that is, the city itself would have an airline to every other city except itself). Since there are n cities, the total number of airlines would be n * (n-1), which is answer choice A.
800 or bust!
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Master | Next Rank: 500 Posts
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by 800_or_bust » Sat May 07, 2016 11:22 am
Max@Math Revolution 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.
Approaching this conceptually, each individual city would have an airline to (n-1) cities (that is, for any given city, that city would have an airline to every other city except itself). Since there are n cities, the total number of airlines would be n * (n-1), which is answer choice A.
800 or bust!
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