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# How many distinct triangles could be drawn using as their vertices thr

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Senior Manager
Joined: 22 Feb 2018
Posts: 427
How many distinct triangles could be drawn using as their vertices thr  [#permalink]

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16 Aug 2018, 21:21
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Difficulty:

45% (medium)

Question Stats:

59% (01:19) correct 41% (01:21) wrong based on 30 sessions

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How many distinct triangles could be drawn using as their vertices three of the vertices of a regular hexagon?

(A) 6
(B) 12
(C) 15
(D) 20
(E) 30

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How many distinct triangles could be drawn using as their vertices thr  [#permalink]

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16 Aug 2018, 21:47
Princ wrote:
How many distinct triangles could be drawn using as their vertices three of the vertices of a regular hexagon?

(A) 6
(B) 12
(C) 15
(D) 20
(E) 30

There are 6 nos of vertices in a regular hexagon. We need any 3 no. of non-collinear points to form a triangle out of 6 points.

So, the #of triangles would be the combination of 3 non-collinear points out of 6 points,
Hence the no of ways of selecting 3 points out of 6 points: $$6C3=\frac{6!}{(6-3)!*3!}=\frac{6!}{3!*3!}=4*5=20$$

Ans. (D)
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How many distinct triangles could be drawn using as their vertices thr   [#permalink] 16 Aug 2018, 21:47
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