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?

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

Quote:

Originally Posted by

**benny92000** 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.

$\displaystyle _6\mathcal{C}_2=\binom{6}{2}=\frac{6!}{2!\cdot 4!}=\frac{6\cdot 5}{2\cdot 1}=15$.

Some of that is what your textbook explained.

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.

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