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# The circle above has 5 points on its edge. How many different quadrila

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The circle above has 5 points on its edge. How many different quadrila  [#permalink]

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03 Apr 2017, 00:35
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The circle above has 5 points on its edge. How many different quadrilaterals can be drawn that use four of these points as its vertices?

A. 120
B. 24
C. 20
D. 5
E. 4

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The circle above has 5 points on its edge. How many different quadrila  [#permalink]

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Updated on: 04 Apr 2017, 18:55
Good Question +1

Option D

Q. states how many quad.s can be formed using given 5 points on a circle a.k.a. Non-collinear points.

4 points can be chosen out of 5 points in 5C4 ways = 5 ways.

PS - Once 4 points are chosen, one draw multiple shapes using them, i.e., closed structures or just lines passing through all 4 points. But, for every chosen set of 4 points there can be only one UNIQUE quad., as order of points while drawing a quad. doesn't matter.

Hence, in total 5 quad.s can be drawn.
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Originally posted by RR88 on 03 Apr 2017, 05:13.
Last edited by RR88 on 04 Apr 2017, 18:55, edited 1 time in total.
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Re: The circle above has 5 points on its edge. How many different quadrila  [#permalink]

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03 Apr 2017, 07:58
Top Contributor
Bunuel wrote:
The circle above has 5 points on its edge. How many different quadrilaterals can be drawn that use four of these points as its vertices?

A. 120
B. 24
C. 20
D. 5
E. 4

Slightly different approach:

IMPORTANT: Connecting any 4 points will create a unique quadrilateral.
So, the question really comes down to "In how many different ways can we select 4 of the 5 points?"
From here, one approach is to calculate 5C4 (as RR88 did)

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

Cheers,
Brent
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Re: The circle above has 5 points on its edge. How many different quadrila  [#permalink]

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06 Apr 2017, 09:29
Bunuel wrote:
The circle above has 5 points on its edge. How many different quadrilaterals can be drawn that use four of these points as its vertices?

A. 120
B. 24
C. 20
D. 5
E. 4

Since the circle 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!(5-4)! = 5.

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Re: The circle above has 5 points on its edge. How many different quadrila  [#permalink]

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08 Apr 2017, 18:43
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Hi All,

The wording of this prompt implies that there should be a picture involved (although whether there's currently a picture there or not, you can draw your own picture and solve this problem without doing ANY complex math whatsoever). Here's how...

1) Draw a circle and place 5 points on its circumference.
2) Label the points A, B, C, D and E.
3) Draw as many unique quadrilaterals (4-sided shapes) using those points as you can (hint: your list will be a short list).

The possible quadrilaterals would be....
ABCD, ABCE, ABDE, ACDE, BCDE. Total = 5

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Re: The circle above has 5 points on its edge. How many different quadrila &nbs [#permalink] 08 Apr 2017, 18:43
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# The circle above has 5 points on its edge. How many different quadrila

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