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

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

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

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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Source: Beat The GMAT — Problem Solving | Wed Jan 03, 2018 12:24 pm

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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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