solve it plz.....?

Question

there are 10 points in a plane, out of which 4 points are collinear.the number of line obtained from the pairs of these points is???

Answer 1

Number of lines for n none collinear points is

L=n(n-1)/2 by deduction
2 points -1 line
3 points - lines
4-points - 6 lines
5-points - 10 lines
6- points - 15 lines and so on

iff m points out of total k points are collinear then n=k-m +1
as if all collinear points become one point
then generating a set of lines with remaining none collinear points

L=m(n(n-1))/2
n=10-4+1=7
L=4(7(7-1))/2=168/2=84 lines

Answer 2

4

Answer 3

Well is 4 points are collinear then you have 6 remaining points to make a line. Since a line requires a minimum of 2 points, the 6 remaining points can make up 3 lines.

3 + 1 = 4 lines.

Answer 4

Answer is
Method 1 ) C(10,2) - C(4,2) + 1 = 40

Method 2) Get lines of the 6 points= C(6,2) = 15
Choose one from collinear points and 1 from the 6 points no of lines = 4 * 6 = 24
There is 1 line which joins all the collinear points so addd one more
Lines = 15 + 24 + 1 = 40

Answer 5

6 x 4+6C2=24 + 15 = 39

No of lines from 4 points to 6 points = 6 x 4 = 24
No of lines formed by 6 points = combination of 6 lines taken 2 at a time = 6C2 = 6(6-1)/2 = 15

total = 24 + 15 = 39

Answer 6

C(2,10) = 45

The 4 collinear would normally count for C(2,4) = 6 of these, but instead they are only 1, therefore we must subtract 5:

45 - 5 = 40

Answer 7

10C2 - 4C2=39