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# Two of the vertices of a regular octahedron are to be chosen at random. What is the probability that they will be the endpoints of an edge o

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Two of the vertices of a regular octahedron are to be chosen at random. What is the probability that they will be the endpoints of an edge of the octahedron? Express your answer as a common fraction.

Apr 5, 2015

#1
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Here's a picture of a  regular octahedron : There are 6 vertices and the number of ways of pairing any two of them is C(6,2)  = 15

But notice that only 12 pairs of them form edges. {The top and bottom vertices aren't connected to each other and neither are the two opposite vertices on the "sides." }

So, the probability that any two form an edge is  12/15 = 4/5   Apr 6, 2015

#1
+10

Here's a picture of a  regular octahedron : There are 6 vertices and the number of ways of pairing any two of them is C(6,2)  = 15

But notice that only 12 pairs of them form edges. {The top and bottom vertices aren't connected to each other and neither are the two opposite vertices on the "sides." }

So, the probability that any two form an edge is  12/15 = 4/5   CPhill Apr 6, 2015
#2
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Hi Chris, That makes sense :)  I like your pic too :)

Apr 6, 2015
#3
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Thanks, Melody......I "stole" that pic from Wikipedia.....LOL!!!   Apr 6, 2015
#4
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I knew that you got it from the web.  It is a good pic.  Pictures make answers so much easier to understand.

They also make answers look 'prettier' and 'pretty' answers are less intimidating to work through. :)

Apr 6, 2015