The number of line segments that can be formed by connecting $10$ points, with no three of them being collinear in all possible ways, is

10

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20

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45

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90

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Solution

The correct option is B $45$
Each line segment is formed by connecting two points. Hence, the number of line segments is equal to the number of selections of 2 points from 10 points. Therefore, number of line segments is $^{10} C_{2}$
= $\frac{10 \times 9}{2 \times 1} = 45$

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The number of line segments that can be formed by connecting 10 points, with no three of them being collinear in all possible ways, is

The correct option is B 45Each line segment is formed by connecting two points. Hence, the number of line segments is equal to the number of selections of 2 points from 10 points. Therefore, number of line segments is 10C2=10×92×1=45

The number of line segments that can be formed by connecting $10$ points, with no three of them being collinear in all possible ways, is

The correct option is B $45$
Each line segment is formed by connecting two points. Hence, the number of line segments is equal to the number of selections of 2 points from 10 points. Therefore, number of line segments is $^{10} C_{2}$
= $\frac{10 \times 9}{2 \times 1} = 45$