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Triangles in a heptagon

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rahulvsd Master | Next Rank: 500 Posts Default Avatar
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Triangles in a heptagon

Post Mon Mar 05, 2012 6:46 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

    ttp://postimage.org/image/59wse2fq5/" target="_blank">

    A.9 B. 21 C. 35 D. 140 E. 210.

    Ans: C. Grockit solves this by using combinations method and I agree with this solution. If the question mentions non-overlapping triangle, will the answer be 5. By using formula (n-2) *180, so here it will be 5 * 180 so 5 triangles, is this approach correct? And if the question was rephrased as number of triangles (does not mention non - overlapping) in a hexagon by the combination method answer will be 6 factorial / 3 factorial * 3 factorial. So 20 triangles, is this correct too? please confirm...

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    pemdas Legendary Member Default Avatar
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    Post Mon Mar 05, 2012 10:58 am
    i selected this option --> one vertice needs two more vertices to form triangle and in total three vertices will be required out of seven, 7C3=35

    c

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    Post Mon Mar 05, 2012 11:14 am
    35 is the answer: 7*6*5/3!

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