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

21

Step-by-step explanation:

In order to form a chord you need to:

Since we have 7 choices for the first point and 6 for the second one, one might think that there are a total of 7*6 = 42 choices.

However the correct answer is 21, because you have to take into the account that selecting the point A first and selecting the point B on second step is the same than selecting the point B first and then the point A, because the chord is the same.

Therefore we are counting each chord twice, and we have to divide the result by 2, obtaining 7*6 / 2 = 21.

You can also calculate the amount by using the combiatorial number. The total amount of possibilities to select k elements from a set of n, with n higher than or equal to k and both positive, without taking into account the order is the combinatorial number of n with k, given by

In this case, in order to form a chord we need to select 2 points of the seven we are given, ignoring order, thus the total amount of possibilities is

As we calculated before.

-81 -56 -27 0 81

step-by-step explanation: