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The circle above has 10 points on its edge. How many different hexagon

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Bunuel
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The circle above has 10 points on its edge. How many different hexagon [#permalink] New post   26 Apr 2017, 08:35
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The circle above has 10 points on its edge. How many different hexagons can be drawn that use six of these points as its vertices?

A. 30,240
B. 1,008
C. 252
D. 210
E. 10


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Re: The circle above has 10 points on its edge. How many different hexagon [#permalink] New post   27 Apr 2017, 05:47
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Bunuel wrote:

The circle above has 10 points on its edge. How many different hexagons can be drawn that use six of these points as its vertices?

A. 30,240
B. 1,008
C. 252
D. 210
E. 10


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A hexagon has 6 vertices.
Since no three points are in a line, we are basically looking for selecting 6 points out of 10..
10C6=\(\frac{10!}{6!4!}=\frac{10*9*8*7}{4*3*2}\)=310

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Re: The circle above has 10 points on its edge. How many different hexagon [#permalink] New post   27 Apr 2017, 09:20
10C6 = 210.

Ans D
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Re: The circle above has 10 points on its edge. How many different hexagon [#permalink] New post   02 May 2017, 16:35
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Bunuel wrote:

The circle above has 10 points on its edge. How many different hexagons can be drawn that use six of these points as its vertices?

A. 30,240
B. 1,008
C. 252
D. 210
E. 10


Since the circle has 10 points on its edge and we need to create hexagons, each of which has 6 vertices, the number of ways to create those quadrilaterals using the 10 points is 10C6:

10!/[6!(10 - 6)!] = 10!/(6! x 4!) = (10 x 9 x 8 x 7)/4! = (10 x 9 x 8 x 7)/(4 x 3 x 2) = 10 x 3 x 7 = 210

Answer: D
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Re: The circle above has 10 points on its edge. How many different hexagon [#permalink]
02 May 2017, 16:35
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