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Two tracks are parallel. The first track has 6 checkpoints and the sec

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Two tracks are parallel. The first track has 6 checkpoints and the sec [#permalink]

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Two tracks are parallel. The first track has 6 checkpoints and the second one has 10 checkpoints. In how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle?

(A)120
(B)150
(C)200
(D)270
(E)420
[Reveal] Spoiler: OA

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Re: Two tracks are parallel. The first track has 6 checkpoints and the sec [#permalink]

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New post 02 Jun 2016, 22:47
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snorkeler wrote:
Two tracks are parallel. The first track has 6 checkpoints and the second one has 10 checkpoints. In how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle?

(A)120
(B)150
(C)200
(D)270
(E)420


To make a triangle, you need 2 checkpoints from one track and 1 from the other. You cannot have all 3 from the same track since then the points will be in a line (assuming straight line of track)

You select 2 checkpoints from the first track and one from the second or two from the second track and one from the first.

6C2 * 10C1 + 10C2 * 6C1 = 150 + 270 = 420

Answer (E)
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Two tracks are parallel. The first track has 6 checkpoints and the sec [#permalink]

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New post 02 Jun 2016, 23:48
snorkeler wrote:
Two tracks are parallel. The first track has 6 checkpoints and the second one has 10 checkpoints. In how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle?

(A)120
(B)150
(C)200
(D)270
(E)420



Two ways this can be done:

a) select any two points on the first track (out of available 6 points) to form the base, and choose the vertex from track B

b) select any two points on the second track (out of available 10 points) to form the base, and choose the vertex from track A


(6C2 * 10C1) + (6C1*10C2)

[\(\frac{6!}{4!2!}\) * 10]+ [\(\frac{6!}{5!1!}\) * \(\frac{10!}{8!2!}\)]

[\(\frac{6 *5}{2}\) * 10]+ 6 * [\(\frac{10 * 9}{2}\)]
= 150+ 270
=420

E is the answer

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Re: Two tracks are parallel. The first track has 6 checkpoints and the sec [#permalink]

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New post 16 Sep 2017, 00:10
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Re: Two tracks are parallel. The first track has 6 checkpoints and the sec   [#permalink] 16 Sep 2017, 00:10
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