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ABCDE is a regular pentagon with F at its center. How many

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ABCDE is a regular pentagon with F at its center. How many [#permalink] New post 27 May 2012, 08:43
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A
B
C
D
E

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  35% (medium)

Question Stats:

64% (01:39) correct 36% (01:19) wrong based on 217 sessions
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Q19.gif
Q19.gif [ 3.29 KiB | Viewed 3557 times ]


ABCDE is a regular pentagon with F at its center. How many different triangles can be formed by joining 3 of the points A, B, C, D, E and F?

A. 10
B. 15
C. 20
D. 25
E. 30
[Reveal] Spoiler: OA
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Re: ABCDE is a regular pentagon with F at its center. How many d [#permalink] New post 27 May 2012, 08:50
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Choosing any 3 points out of the 6 available points will form a triangle. Hence this turns into a combination question.

Choose 3 points out of 6: 6c3=20 :)
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Re: ABCDE is a regular pentagon with F at its center. How many [#permalink] New post 28 May 2012, 00:03
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macjas wrote:
Attachment:
Q19.gif


ABCDE is a regular pentagon with F at its center. How many different triangles can be formed by joining 3 of the points A, B, C, D, E and F?

A. 10
B. 15
C. 20
D. 25
E. 30


Generally in a plane if there are n points of which no three are collinear, then:
1. The number of triangles that can be formed by joining them is C^3_n.

2. The number of quadrilaterals that can be formed by joining them is C^4_n.

3. The number of polygons with k sides that can be formed by joining them is C^k_n.

Since ABCDE is a regular pentagon then no three point out of 6 (5 vertices + center) will be collinear, so the number of triangles possible is C^3_6=20.

Answer: C.

Similar questions to practice:
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Hope it helps.
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Re: ABCDE is a regular pentagon with F at its center. How many [#permalink] New post 10 Jun 2012, 00:44
some body please clear this discrepancy

from 6 if we choose 3 , how do we denote it , all books and materials show this as 6C3

but here parrot man shows this as 6c3 and moderator shows this as 3c6 , leading me to becoming confused !!

according to me , the larger one goes at the top and the smaller sub group goes below

so from 6 if we choose 3 then 6C3.

so please if someone could confirm why is 3C6 denoted here , and does 3C6 mean the same as 6C3 ? are they same ?

so from n if if have to choose , 3 or 4 or 5 etc shouldn't it be nc3 , nc4 , nc5 etc .... Please clear my confusion
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Re: ABCDE is a regular pentagon with F at its center. How many [#permalink] New post 10 Jun 2012, 02:09
There are many forms of denoting the combinations.

nCk or C(n,k) or Ckn as written by bunuel, all are different standards.

But the meaning is same. Choosing 'k' objects from a group of 'n' objects.
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Re: ABCDE is a regular pentagon with F at its center. How many [#permalink] New post 23 Sep 2013, 21:50
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Re: ABCDE is a regular pentagon with F at its center. How many [#permalink] New post 03 Jan 2014, 16:47
macjas wrote:
Attachment:
Q19.gif


ABCDE is a regular pentagon with F at its center. How many different triangles can be formed by joining 3 of the points A, B, C, D, E and F?

A. 10
B. 15
C. 20
D. 25
E. 30



Combination Q; hw many ways to select 3 points from a group of 6 points . 6C3 = 6*5*4*3! / 3!*6 = 20

OA=C

Thanks for posting

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Re: ABCDE is a regular pentagon with F at its center. How many   [#permalink] 03 Jan 2014, 16:47
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