There are $n$ lines in a plane, no two of which are paralel, and no three are concurrent. Their points of intersection are joined. The number of fresh line thus obtained is

\frac{n (n - 1) (n - 2) (n - 3)}{8}

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\frac{n (n + 1) (n - 1) (n - 2)}{8}

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\frac{n (n - 1) (n - 2) (n - 3)}{6}

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\frac{n (n - 1) (n - 2)}{8}

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Solution

The correct option is A $\frac{n (n - 1) (n - 2) (n - 3)}{8}$
The number of point of intersection $=^{n} C_{2} = \frac{n (n - 1)}{2!}$
The number of fresh lines $=$
$^{\frac{n (n - 1)}{2}} C_{2} - n = \frac{n (n - 1) (n - 2) (n - 3)}{8}$

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There are n lines in a plane, no two of which are paralel, and no three are concurrent. Their points of intersection are joined. The number of fresh line thus obtained is

The correct option is A n(n−1)(n−2)(n−3)8The number of point of intersection =nC2=n(n−1)2! The number of fresh lines = n(n−1)2C2−n=n(n−1)(n−2)(n−3)8

There are $n$ lines in a plane, no two of which are paralel, and no three are concurrent. Their points of intersection are joined. The number of fresh line thus obtained is

The correct option is A $\frac{n (n - 1) (n - 2) (n - 3)}{8}$
The number of point of intersection $=^{n} C_{2} = \frac{n (n - 1)}{2!}$
The number of fresh lines $=$
$^{\frac{n (n - 1)}{2}} C_{2} - n = \frac{n (n - 1) (n - 2) (n - 3)}{8}$