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?