Question

How many lines are determined by the points a b c d and e if 3 of them arent collinear

Answer 1

10 possible lines

Explanation:

Given

`Points = \{a,b,c,d,e\}`

Required

Number of lines

From the question, the number of points (n) are:

`n = 5`

If 3 points are not collinear (i.e. on a straight line), it means that only (5 - 3) of the points can be chosen

So, we have:

`n = 5`

`r = 5 - 3`

`r =2`

The number of lines is then calculated using combination formula.

`^nC_r = (n!)/((n-r)!r!)`

We used combination because the analysis done above implies that 2 points are to be selected from a,b,c,d and e.

To select means combination

Having said that;

Substitute
`5\ for\ n\ and\ 2\ for\ r`

`^5C_2 = (5!)/((5-2)!2!)`

`^5C_2 = (5!)/(3!2!)`

`^5C_2 = (5*4*3!)/(3!2!)`

`^5C_2 = (5*4)/(2!)`

`^5C_2 = (5*4)/(2*1)`

`^5C_2 = (20)/(2)`

`^5C_2 = 10`

Hence, there are 10 possible lines