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01 Sep 2017, 00:47
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
71% (00:45) correct
29%
(01:04)
wrong
based on 62
sessions
History
Date
Time
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Not Attempted Yet
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 3500 times ]
01 Sep 2017, 01:01
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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)
07 Sep 2017, 07:16
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Bunuel
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.
Answer: D
