Seven points are marked on the circumference of a circle. How many different chords can be drawn by connecting two of these seven points?
Instead of circles and whatnot, we can instead call this a "heptagon"
AKA this shape:
Anyways, we can reword this question: How many diagonals / sides does a 7-sided heptagon have?
Sure, you can go draw all the lines. I'll wait for you. But there is a quicker, mathematical way to do it.
We see that there are 7 dots to choose from. From these 7 points, how many more points can we use to choose the second dot? There are 7 - 1 = 8 points (because you can't your original point)
Now, we multiply:
7 x 8 = 56
But, remember, the order does not matter! This means that we need to divide by 2! to cancel out the repeats.
56/2! = 56/2 = 28 diagonals / chords <------ answer that guest got!
have you finished drawing the lines yet? if i were you, i would not draw 28 lines!