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connecting lines

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connecting lines [#permalink]

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New post 21 Apr 2010, 01:31
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In a certain province in France there are 15 villages. How many roads are required in order to connect each village to all of the others?

[Reveal] Spoiler:
105
1 KUDOS received
Senior Manager
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Joined: 19 Nov 2009
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Kudos [?]: 81 [1] , given: 44

Re: connecting lines [#permalink]

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New post 21 Apr 2010, 01:44
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It's 105..

The formula used is : n * (n-1) /2 --> 15 * 14 / 2 --> 105
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Re: connecting lines [#permalink]

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New post 21 Apr 2010, 11:11
no: of ways of selecting 2 villages among 15 = 15C2 = 105 :idea:
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Re: connecting lines [#permalink]

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New post 21 Apr 2010, 22:11
sudai wrote:
In a certain province in France there are 15 villages. How many roads are required in order to connect each village to all of the others?

[Reveal] Spoiler:
105

hi,
to connect 2 villages, we need to select 2 of them out of 15.
that can be done in 15C2 ways = 105 ways.
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fivezero7

Re: connecting lines   [#permalink] 21 Apr 2010, 22:11
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