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There are 10 points on a circle. A hexagon . . . . .

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by Vincen » Wed Jan 03, 2018 12:24 pm
There are 10 points on a circle. A hexagon can be formed by linking 6 of the 10 points. How many such hexagons are possible?

A. 60
B. 120
C. 200
D. 210
E. 600

The OA is the option D.

How can I get the total number of hexagons? I don't know how can I count all the hexagons. Thanks in advanced.
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by DavidG@VeritasPrep » Wed Jan 03, 2018 4:37 pm
Vincen wrote:There are 10 points on a circle. A hexagon can be formed by linking 6 of the 10 points. How many such hexagons are possible?

A. 60
B. 120
C. 200
D. 210
E. 600

The OA is the option D.

How can I get the total number of hexagons? I don't know how can I count all the hexagons. Thanks in advanced.
Mathematically, this question is identical to asking, "In a group of 10 students, 6 must be chosen to form a sub-comittee. How many 6-person subcommittees are possible." The upshot is that we're selecting 6 elements from a population of 10 and order doesn't matter, so we're looking for 10C6: (10*9*8*7*6*5)/6! = (10*9*8*7*6*5)/6*5*4*3*2*1 (terms in red cancel)= (10*9*8*7*5)/5*4*3*2*1 = 9*8*7*5/4*3*1 = 3*2*7*5 = 210.
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by Scott@TargetTestPrep » Mon Sep 02, 2019 6:08 pm
Vincen wrote:There are 10 points on a circle. A hexagon can be formed by linking 6 of the 10 points. How many such hexagons are possible?

A. 60
B. 120
C. 200
D. 210
E. 600

The OA is the option D.

How can I get the total number of hexagons? I don't know how can I count all the hexagons. Thanks in advanced.
The total number of hexagons can be created in 10C6 ways:

10! / (6! x 4!)

(10 x 9 x 8 x 7 x 6 x 5) / (6 x 5 x 4 x 3 x 2)

(10 x 9 x 8 x 7) / (4 x 3 x 2)

10 x 3 x 7 = 210

Answer: D

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