Avijit Arya
Last Activity: 15 Years ago
Hi,
For two points, one line can be drawn. For 3 points, 3 different lines can be drawn, on the condition that these points are not collinear, otherwise only single line will be drawn. Generalizing this, we can conclude that, for n number of points, we can draw a max. of nC2 lines. In this Q., there are 10 points, of which max. of 10C2, or 45 lines can be drawn. However, since 4 of these points are collinear, we have to subtract, the total no. of lines formed by these points, if they were not collinear, as that case is also included in the max. 45 lines formed. So subtracting 4C2 from 10C2 gives you =45-6=39 lines. Here we have subtracted all possible lines formed by those 4 points, however 1 line is formed by those 4 points, since they are collinear, so only 1 line is formed. So finally we have to add 1 line to the total we have got, that is 39. Hence the answer here is, 10C2-4C2+1=45-6+1= 40 lines, is the answer.
Thanks