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# How many different line segments can be drawn to connect all possible

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Math Expert
Joined: 02 Sep 2009
Posts: 46207
How many different line segments can be drawn to connect all possible [#permalink]

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01 Sep 2017, 00:47
00:00

Difficulty:

35% (medium)

Question Stats:

70% (00:31) correct 30% (00:42) wrong based on 44 sessions

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How many different line segments can be drawn to connect all possible pairs of points shown above?

(A) 32
(B) 25
(C) 20
(D) 10
(E) 5

Attachment:

2017-09-01_1134_003.png [ 3.72 KiB | Viewed 723 times ]

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Re: How many different line segments can be drawn to connect all possible [#permalink]

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01 Sep 2017, 01:01

Since we have a total of 5 points,
and a line segment can be formed when a pair of points are connected.

We can have a total of 5c2 line segments possible, which is $$\frac{5*4}{2} = 10$$(Option D)
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Re: How many different line segments can be drawn to connect all possible [#permalink]

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07 Sep 2017, 07:16
Bunuel wrote:

How many different line segments can be drawn to connect all possible pairs of points shown above?

(A) 32
(B) 25
(C) 20
(D) 10
(E) 5

Attachment:
2017-09-01_1134_003.png

Since each line segment has two vertices, the number of lines that can be drawn is 5C2 = 5!/[2!(5-2)!] = 5!/(2!3!) = (5 x 4)/2! = 10.

Alternate Solution:

Let’s start with the point A. We see that the segments are AB, AC, AD, and AE. Now let’s progress to point B. The segments are BC, BD, and BE (noting that we don’t need BA because we already had AB). Similarly, with point C, we have CD and CE. Finally, for point D, we have only DE. This is a total of 4 + 3 + 2 + 1 = 10 segments.

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Re: How many different line segments can be drawn to connect all possible [#permalink]

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07 Sep 2017, 09:21
Bunuel wrote:

How many different line segments can be drawn to connect all possible pairs of points shown above?

(A) 32
(B) 25
(C) 20
(D) 10
(E) 5

Attachment:
2017-09-01_1134_003.png

Since there are 5 points, the number of lines that can be drawn is given by 5C2 = 10 (D)
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Re: How many different line segments can be drawn to connect all possible [#permalink]

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07 Sep 2017, 10:18

Number of ways you choose 2 from 5 (because you're connecting two points from 5 points each time):

5!/2!3! = 5(4)/2 = 10.
Re: How many different line segments can be drawn to connect all possible   [#permalink] 07 Sep 2017, 10:18
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# How many different line segments can be drawn to connect all possible

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