Eight points are placed on a circle. How many lines are possible if each point is connected to each of the other points
each of the 8 points is connected to the other 7
8 * 7 = 56 ... BUT ... a line from A to B is the same as a line from B to A ... so 56/2
there are 8 ways to choose the 1st point
for each of those, there are 7 points to connect to.
But, after all that, you've picked each point twice.
To determine the number of possible lines that can be drawn between the eight points on a circle, we need to use a combination formula.
First, we need to choose two points out of the eight to form a line. Since the order of the points does not matter (connecting point A to point B is the same as connecting point B to point A), we need to use the combination formula instead of the permutation formula.
The formula for combination is:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to take at a time.
In this case, n = 8 (the total number of points) and r = 2 (we want to choose two points at a time).
Using the combination formula, we can calculate the number of possible lines:
C(8, 2) = 8! / (2!(8-2)!) = 8! / (2!6!) = (8 * 7) / (2 * 1) = 28
Therefore, there are 28 possible lines that can be drawn between the eight points on the circle.