How many line are determined by 15 points, no 3 of them being collinear?

Question

A) 15
B) 105
C) 1365
D) 210

Please explain your answer...

Answer 1

Since no three of the points are colinear, every pair of points determines a unique line. The number of pairs of points is: 15 choose 2 = 15*14/2 = 105, so the number of lines is 105.

Answer 2

This just means how many pairs of points are there? If no three are collinear, then every pair represents a line.

If you like, you can say there are 14 lines through every point (14 other points to join it to). Multiply this by 15, since it applies to each of the 15 points. But that means we've counted every line twice, because if two of the points are called A and B, we counted AB as a line through A and also as a line through B. So we must divide the answer by 2. Notice answer B) is half of answer D).

Answer 3

Since no 3 points are colinear, any two of them form a distinct line. Thus the number of lines is equal to the number of distinct ways to choose 2 points out of the 15. How many ways can you choose two points out of 15? Well there are 15 ways to choose the first point, and 14 ways to choose the second, and thus 15*14 ways to choose a first and second point. However, it doesn't matter what order you choose them in, so you divide by 2 to get 15*7 = 105.

Answer 4

because each line uses up two points, there for 15 points gives you a start of 14 lines.

14+13+12+11+......+1 gives you the total of lines.

when you are finished with each starting point and move onto the next, you do not repeat the ones connecting to any of the previous points. This is why i add one less every time.

Answer 5

105.
Number the points 1-15.
Point #1 can be connected to 14 other points to make a line.
Point #2 can be connected to 13 other points (you can't connect it to Point #1 because you already connected those two points in the first step)
Point #3 can be connected to 12 other points...
...
Point #14 can be connected to 1 other point
Point #15 can be connected to no more points (you already connected all the points to #15 already).
14+13+12+11...+1=105

Answer 6

1365