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
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  • 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?



    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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