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# Counting Pairs

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Seven points are marked on the circumference of a circle. How many different chords can be drawn by connecting two of these seven points?

Aug 31, 2020

#1
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The number of possible chords is 28.

Aug 31, 2020
#2
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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!

:)

Aug 31, 2020
edited by ilorty  Aug 31, 2020