Q92 / 160 · TS EAMCET 2014 · Mathematics

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

A
$296$
B
$540$
Correct answer
C
$408$
D
$348$

Solution

Total number of points in a plane is 30 . Out of them, 8 points are collinear. $\therefore$ Total number of straight lines formed $$ \begin{aligned} & ={ }^{30} C_2-{ }^8 C_2+1 \\ & =\frac{30 \times 29}{2}-\frac{8 \times 7}{2 \times 1}+1 \\ & =435-28+1=408 \end{aligned} $$

Hence, the correct answer is option: 'C'.

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