Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be…
Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be formed by joining these points, is
$296$
$540$
$408$
$348$
Solution
Total number of points in a plane is 30 . Out of them, 8 points are collinear. $\therefore$ Total number of straight lines formed
$
\begin{aligned}
& ={ }^{30} C_2-{ }^8 C_2+1 \\
& =\frac{30 \times 29}{2}-\frac{8 \times 7}{2 \times 1}+1 \\
& =435-28+1=408
\end{aligned}
$