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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
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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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