How many different chords can be drawn between 20 distinct points on a circle?

I'm not sure how my book got 190?

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- Mar 30th 2010, 07:56 PMdannycnumber of chords
How many different chords can be drawn between 20 distinct points on a circle?

I'm not sure how my book got 190? - Mar 30th 2010, 08:16 PMsa-ri-ga-ma
- Mar 30th 2010, 08:27 PMintegral
$\displaystyle \sum^{19}_{n=0}n=c$

Draw 10 points on one side of a circle and 10 on the other.

The first point as the choice between 19 points to form a chord.

Once formed, this takes 1 choice from all other points.

And so on.

Therefore it equals the above.

And any number of points has the following number of chords.

$\displaystyle \sum^{i}_{n=0}n=c$

where i is the number of points minus 1 due to the lack of self choice. - Mar 30th 2010, 10:24 PMdannyc
Hmm I still don't see it guys.. so I use the formula for a combination? (As opposed to a permutation?)

- Mar 31st 2010, 12:57 AMHallsofIvy
Is that how you learn mathematics? Memorizing formulas rather than

**thinking**about a problem?

If there are 20 points, then there are 19 chords connecting each point to the 19 others. If each chords were different, there would be 20(19) of them. But they are not- each chord involves 2 points so that is twice as large as it should be- correct by dividing by 2: 20(19)/2= 10(19) as sa-ri-ga-ma said. - Mar 31st 2010, 01:06 AMdannyc
Hence the newbie status--we all can't be an expert..