Question

There are 15 points in a plane and 5 of them are collinear. The number of straight lines
joining any two points is:
(a) 45
(b) 86
(c) 76
(d) 96​

Answer 1

96

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Answer 2

The number of straight lines joining any two points that can be drawn from 15 points in a plane and 5 of the lines are collinear is 96.

As per the question given,

The number of straight lines that can be drawn between 15 points is given by the formula for combinations, which is: C(15,2) = 15! / (2! * (15-2)!).

However, we need to subtract the number of lines that can be drawn through the 5 collinear points. To do this, we can calculate the number of lines that can be drawn between these 5 points: C(5,2) = 5! / (2! * (5-2)!).

Finally, the total number of lines is: C(15,2) - C(5,2) = 15! / (2! * (15-2)!) - 5! / (2! * (5-2)!).

The answer is (d) 96.

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