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Math Help - Combinatorial argument and how many intersections?

  1. #1
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    Combinatorial argument and how many intersections?

    1. Use a combinatorial argument to show that with



    2. We are given points arranged around a circle and the chords connecting each pair of points are drawn. If no three chords meet in a point, how many points of intersection are there? For example, when there are intersections.

    Thanks!

    I just started combinatorics so please don't leave out any necessary steps! Thanks again
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  2. #2
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    Quote Originally Posted by usagi_killer View Post
    1. Use a combinatorial argument to show that with



    2. We are given points arranged around a circle and the chords connecting each pair of points are drawn. If no three chords meet in a point, how many points of intersection are there? For example, when there are intersections.

    Thanks!

    I just started combinatorics so please don't leave out any necessary steps! Thanks again
    do not post your questions in wrong subforums! this question is a "discrete math" question not abstract algebra.
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  3. #3
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    Q1: How many ways can we choose k things from m+n things? Split the m+n bunch into a group of m things and a group of n things. Then you could choose the k things by choosing 0 from the n group and k from the m group. Or you could choose 1 thing from the n group and k-1 from the m group.
    Or you could choose 2 things from the n group and k-2 from the m group.
    etc.
    How many ways are there of doing these? That's your sum.

    Q2. Any 4 points determine 1 intersection point. Think 2 intersecting chords from 4 points. So you've determined n choose 4 points.
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