ABCDEFGH is an octagon. Two vertices of the octagon are selected

Question

ABCDEFGH is an octagon. Two vertices of the octagon are selected at random. Find the probability that these vertices form a diagonal of the octagon.

A.  \frac{1}{7}

B.  \frac{2}{7}

C.  \frac{3}{7}

D.  \frac{4}{7}

E.  \frac{5}{7}

IanStewart · Accepted Answer

A diagonal of a polygon is any line connecting two vertices that is not an edge, so an octagon has quite a few diagonals -- I think you're only counting lines connecting vertices that are strictly opposite each other.

Here we can select a pair of vertices in 8*7/2! = 28 ways. If we draw a line between our pair of vertices, it will be a diagonal unless it's one of the 8 edges of the octagon. So we can draw 28 - 8 = 20 diagonals, and the answer is 20/28 = 5/7.

nick1816 · Answer

Number of ways you can select 2 verices= 8C2=28
Number of ways these vertices form a diagonal= nC2-n=8C2-8=20

the probability that these vertices form a diagonal of the octagon. = 20/28=5/7

nick1816 · Answer

My bad!! Gotta edit my solution.

harshrd94 · Answer

The total no of diagonals for a n-sided polygon can be given by the formula- (n(n-3))/2.
so in this case total no of diagonals= 8(8-3)/2=20 diagonals

Total no. of ways of selecting 2 points out of 8= 8C2=28 ways

Thus required probability=20/28=5/7

Thus E is the right answer

philipssonicare · Answer

Octagon has 8 vertices. Probability of picking the first vertex is 8/8 (doesn't matter which one).
Then there are 7 other vertices (x/7). Can't pick the one adjacent left or adjacent right as those are not diagonal.
(7-2)/7=5/7

CrackverbalGMAT · Answer

SOLUTION

The question is of selection as order is NOT important here. Selecting vertices A and B is same as B and A.

Number of ways to select two vertices is 8C2 =28. This is our total sample space or S.

Of these 28, 8 will be the sides of the octagon itself
Excluding them, the rest of the 20 are diagonals.
(We can also use the formula nC2 - n =Diagonals in a polygon)

Thus the required probability = 20/28 = 5/7 (OPTION E)

Hope this helps

Devmitra Sen(Math)

Akshaynandurkar · Answer

Total ways to select the 2 points from 8 points = 8C2 = 28
and to form diagonal of octagon, we can't select adjacent points. so if we select any point of octagon we have total 5 choices to select other point.
so total no of ways to select points such that it forms diagonal = 8 x (1c1 x 5c1) / 2 (since selecting two points AC is same as selecting CA, we need to take half of the total )

probability = 20/28 = 5/7

dhruva09 · Answer

Bunuel  can you confirm if such questions can be expected on the gmat focus ?

Bunuel · Answer

________________
Probably not.

ABCDEFGH is an octagon. Two vertices of the octagon are selected

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ABCDEFGH is an octagon. Two vertices of the octagon are selected

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