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

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

Permutations and Combinations

Solution:

Reqd. number of st. lines
$=^{18}C_{2}-^{5}C_{2}+1=\frac{18\times17}{12}-\frac{5\times4}{2}+1$
$=153-10+1$
$=144$