AP EAMCET · Maths · Permutation Combination
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 \(540\)
- C \(408\)
- D \(348\)
Answer & Solution
Correct Answer
(C) \(408\)
Step-by-step Solution
Detailed explanation
Total number of points in a plane is 30 . Out of them, 8 points are collinear. \(\therefore\) Total number of straight lines formed \[ \begin{aligned} & ={ }^{30} C_2-{ }^8 C_2+1 \\ & =\frac{30 \times 29}{2}-\frac{8 \times 7}{2 \times 1}+1 \\ & =435-28+1=408 \end{aligned} \]
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