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

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

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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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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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