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

• Nov 6th 2011, 02:34 PM
benny92000
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?
• Nov 6th 2011, 02:50 PM
Plato
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.
• Nov 6th 2011, 02:54 PM
benny92000
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.
• Nov 6th 2011, 07:37 PM
Wilmer
Re: How many chords can be drawn from two points on circumference of a circle?