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Bunuel
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In a certain province in France there are 15 cities. If a single road 06 Nov 2023, 02:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

60% (01:23) correct 40% (01:32) wrong based on 274 sessions

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In a certain province in France there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?

A. 30
B. 105
C. 330
D. 14!
E. 15!


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B
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cdrectenwald
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In a certain province in France there are 15 cities. If a single road 06 Nov 2023, 03:23
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Would this be 15 choose 2 so 15*7 = 105?

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Introvertuprising
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In a certain province in France there are 15 cities. If a single road 06 Nov 2023, 05:29
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Take 3 cities A,B,C single road connects two cities

A-B
B-C
C-A
n(n-1)/2 =3*2/2 =3

For 15 cities
15*14/2 =105
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In a certain province in France there are 15 cities. If a single road 06 Nov 2023, 11:43
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Bunuel
In a certain province in France there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?

A. 30
B. 105
C. 330
D. 14!
E. 15!


Show more

OA is B

For this type of questions to make sure whether combination will work or not. Always start with less city and eventually go to more city.
We started with 2 city only one road,
Similarly we can increase more as described below

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In a certain province in France there are 15 cities. If a single road 22 Dec 2023, 00:39
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cdrectenwald
Would this be 15 choose 2 so 15*7 = 105?

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Let's understand by taking examples.
1. Take three cities A, B, and C. What are the possible roads? AB, AC, BC.
2. Take four cities A, B, C, and D. What are the possible roads now? AB, AC, AD, BC, BD, CD.
In each case, we can see the possible number of roads is nC2 where n = number of cities. Put n=15 and answer in 105.
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In a certain province in France there are 15 cities. If a single road 25 Jan 2025, 08:27
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