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Math Help - How many chords can be drawn from two points on circumference of a circle?

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    How many chords can be drawn from two points on circumference of a circle?

    If A, B, C, D, E, and F are 6 distinct points on the circumference of a circle, how many different chords can be drawn using any 2 of the points?

    The answer is 15. My book says the following: "Each point is connected to five other points to make 5 chords per unit. But this counts every chord twice--AB is indistinguishable from BA--so after you multiply 6 by 5, you have to divide by 2."

    I don't get where the 6 comes from or why you multiply. I originally got 9. 5 for the first and 4 for the next. What am I missing?
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    Re: How many chords can be drawn from two points on circumference of a circle?

    Quote Originally Posted by benny92000 View Post
    If A, B, C, D, E, and F are 6 distinct points on the circumference of a circle, how many different chords can be drawn using any 2 of the points?
    This a simple combinations question.
    _6\mathcal{C}_2=\binom{6}{2}=\frac{6!}{2!\cdot 4!}=\frac{6\cdot 5}{2\cdot 1}=15.

    Some of that is what your textbook explained.
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    Re: How many chords can be drawn from two points on circumference of a circle?

    I think I misunderstood the question. I took two of the 6 points--say points A and B--and I drew chords from each of those points.. So I guess that's not what it's asking to do.

    I thought it was obvious that a chord would be 2 points.
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    Re: How many chords can be drawn from two points on circumference of a circle?

    ab,ac,ad,ae,af
    bc,bd,be,bf
    cd,ce,cf
    de,df
    ef
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