Question

Any 2 points determine a line. If there are 6 points in a plane, no 3 of which lie on the same line, how many lines are determined by pairs of these 6 points?

Answer 1

Total number of lines formed by 6 points will be 15.

Explanation:

Number of lines determined by 2 points = 1

There is a condition that only 2 points lie on a line.

Total number of points on a plane = 6

We have to calculate the number of lines formed by the pairs of these 6 points.

It's a question of combinations.

Number of combinations formed =
`^(6)C_(2)`

=
`(6!)/((6-2)!2!)`

=
`(6* 5* 4!)/(4!* 2!)`

=
`(30)/(2* 1)`

= 15

Therefore, total number of lines formed by 6 points will be 15.