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# There are 18 points in a plane of which 5 are collinear. How many straight lines can be formed by joining them?

Answer :

A line is formed by joining two points.

If the total number of points is 18, the total number of lines would be = ^{18}C_{2}

But 5 points are collinear, so the lines made by these points are the same and would be only 1.

Hence there is 1 common line joining the 5 collinear points.

As these 5 points are also included in 18 points so these must be subtracted from the total case , i.e. ^{5}C_{2} must be subtracted from ^{18}C_{2 .}

Finally, the number of straight line = ^{18}C_{2} - ^{5}C_{2} + 1

= 144 lines

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