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

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.

Tardigrade Admin · Accepted Answer

Reqd. number of st. lines =18C2-5C2+1=(18×17/12)-(5×4/2)+1 =153-10+1 =144

Q. 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

143

144

153

none of these.

Reqd. number of st. lines
$=^{18} C_{2} -^{5} C_{2} + 1 = \frac{18 \times 17}{12} - \frac{5 \times 4}{2} + 1$
$= 153 - 10 + 1$
$= 144$

Q. 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

143

144

153

none of these.

Reqd. number of st. lines =18C2​−5C2​+1=1218×17​−25×4​+1 =153−10+1 =144

Reqd. number of st. lines
$=^{18} C_{2} -^{5} C_{2} + 1 = \frac{18 \times 17}{12} - \frac{5 \times 4}{2} + 1$
$= 153 - 10 + 1$
$= 144$