There are 10 points in a plane, no three of which are in the same straight line, except 4 points, which are collinear.
Find the number of lines obtained from the pairs of these points,

Options

A. 40
B. 39
C. 45
D. none of these

Answer

A

Explanation

Number of stright lines formed joining the 10 points, taking 2 at a time
`""^(10)C_(2)=(10!)/(2!8!)=45`.
Number of straight lines formed by joining the four points, taking 2 at a time
`""^(4)C_(2)=(4!)/(2!2!)=6`
But, 4 collinear points, when joined pairwise give only one line.
`:.` Required number of straight lines =45-6+1=40.