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There are $n$ -points $(n > 2)$ in each of two parallel lines. Every point on one line is joined to every point on the other line by a line segment drawn within the lines. The number of points (between the lines) in which these segments intersect is,

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$^{2 n} C_{2} - 2 \times^{n} C_{2}$

$^{2 n} C_{2} - 2 \cdot^{n} C_{1} + 2$

none of these

$^{n} C_{2} \times^{n} C_{2}$

answer is C.

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Detailed Solution

We observe that a point is obtained between the lines if two of points on first line are joined by line segments to two points on the second line.

Hence, required number of points $=^{n} C_{2} \times^{n} C_{2}$ .

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