There are $10$ points in a plane of which $4$ are collinear, the maximum number of straight line the can be drawn from these points will be

49

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45

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46

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36

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Solution

The correct option is B $45$
Number of points $= 10$
$4$ Are collinear
$6$ are non-collinear
Number of lines formed with non collinear points $=^{6} C_{2}$
$= \frac{6 \times 5}{2} = 15$
Number of lines formed with collinear points $= =^{4} C_{2} = 6$
$^{6} C_{1} \times^{4} C_{1} = 24$
Total number of lines $= 24 + 15 + 6 = 45$ lines

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IS THERE ANY FORMULA FOR THIS KIND OF QUESTIONS?

There are 10 points in a plane no three of which are in the same straight line, excepting 4 points, which are collinear.

Find the probability that

(i) number of straight lines obtained from the pairs of these points.

(ii) number of triangles that can be formed with the vertices as these points.

11

4

10

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