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Question
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
Options
45
40
39
38
Solution
40
Number of straight lines formed by joining the 10 points if we take 2 points at a time =\[{}^{10} C_2 = \frac{10}{2} \times \frac{9}{1} = 45\]
Number of straight lines formed by joining the 4 points if we take 2 points at a time =\[{}^4 C_2 = \frac{4}{2} \times \frac{3}{1} = 6\]\
But, 4 collinear points, when joined in pairs, give only one line.
∴ Required number of straight lines =\[45 - 6 + 1 = 40\]
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