Question

Out of 18 points in a plane, no three are in the same st. line except five points which are collinear. The number of straight lines that can be formed joining them is

• A. 143
• B. 144
• C. 153
• D. none of these.

Answer 1

Answer: (B)

144

Answer 2

Reqd. number of st. lines $=^{18}C_{2}-^{5}C_{2}+1=\frac{18\times17}{12}-\frac{5\times4}{2}+1$ $=153-10+1$ $=144$