How many different quadrilaterals can be formed if lines are drawn con

Question

How many different quadrilaterals can be formed if lines are drawn connecting the vertices of a regular pentagon?

A. 1
B. 4
C. 5
D. 6
E. 10

BrentGMATPrepNow · Answer

IMPORTANT: Connecting any 4 of pentagon's 5 vertices will create a unique quadrilateral. 
So, the question really comes down to "In how many different ways can we select 4 of the 5 vertices?" 
From here, one approach is to calculate 5C4 (which equals 5)

Another approach is to recognize that, if we select 1 vertex and REMOVE IT, then we are left with 4 vertices, which can be connected to create a unique quadrilateral.
So, in how many different ways can we select 1 vertex to REMOVE? 
There are 5 vertices, so there are 5 ways to select 1 vertex.

Answer:  C

Cheers,
Brent

anuk44 · Answer

Since its selection, we use combinations.

selecting 4 points ( for quad ) out of 5 points ( pentagon) = 5C4 ways= 20.

Therefore, 20 different quadrilateral can be formed

JeffTargetTestPrep · Answer

Since a pentagon has 5 points on its edge and we need to create quadrilaterals, each of which has 4 vertices, the number of ways to create those quadrilaterals using the 5 points is:

5C4 = 5!/4!1! = 5

Answer: C

InfiniteLoop80 · Answer

I was tricked by the wording of this question. I understood the question as : lines are drawn from the vertices, then we count the number of quadrilaterals after that. This would include quadrilaterals that have each vertex as one of the vertex of the original pentagon vertices, AND quadrilaterals that have some vertices the intersection between the newly drawn lines.
Hence , to me the answer was : 5C4(for the first case, quads drawn with each vertex as vertex of the pentagon) + additional quads with atleast one vertex not part of the original pentagon vertex.

Any thoughts about the wording of the problem?

FlyingCycle · Answer

no of diagonal formula = n(n-3)/2 
where n is the number of sides

How many different quadrilaterals can be formed if lines are drawn con

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How many different quadrilaterals can be formed if lines are drawn con

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