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there are 10 points in a plane of which 4 are collinear.
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how many diff. straight lines can be drawn by joining these points..

(please explain the answer by using permutation combination)

7 years ago

Dear ajinkyastraight line can be formed by joining 2 points

so number of ways in which we can select 2 points from 10 points is =

^{10}C_{2}but it also include that in which 4 points are in straight line . from those 4 points only one line can be formed .

so we have to subtract

^{4}C_{2}-1 from above resultso total lines are =

^{10}C_{2 - }^{4}C_{2}+ 1

^{Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE & AIEEE preparation. All the best. Regards,Askiitians ExpertsBadiuddin}

7 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

7 years ago

How many different straight lines can be formed by joining 12 different points on a plane of which four are collinear and the rest are non collinear?

7 months ago

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