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

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Math Expert
Joined: 02 Sep 2009
Posts: 52164
The circle above has 10 points on its edge. How many different hexagon  [#permalink]

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26 Apr 2017, 07:35
00:00

Difficulty:

15% (low)

Question Stats:

88% (00:53) correct 13% (01:07) wrong based on 53 sessions

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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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image007.gif [ 620 Bytes | Viewed 762 times ]

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Posts: 7199
Re: The circle above has 10 points on its edge. How many different hexagon  [#permalink]

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27 Apr 2017, 04:47
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

Attachment:
image007.gif

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

D
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Re: The circle above has 10 points on its edge. How many different hexagon  [#permalink]

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27 Apr 2017, 08:20
10C6 = 210.

Ans D

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Re: The circle above has 10 points on its edge. How many different hexagon  [#permalink]

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02 May 2017, 15:35
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

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Re: The circle above has 10 points on its edge. How many different hexagon &nbs [#permalink] 02 May 2017, 15:35
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