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  4. Out of 18 points in a plane, no three are in the same line except five points which are collinear. The number of lines that can be formed joining these points are

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Q. Out of 18 points in a plane, no three are in the same line except five points which are collinear. The number of lines that can be formed joining these points are

Permutations and Combinations

Solution:

Number of lines that can be formed on joining 18 non-collinear points $={ }^{18} C _2$
Number of lines formed by joining 5 collinear points is only 1.
Number of lines if the 5 points have been non-collinear
$={ }^5 C _2$
Required number of lines $={ }^{18} C _2-{ }^5 C _2+1$