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how many diff. straight lines can be drawn by joining these points..

(please explain the answer by using permutation combination)

11 years ago

**Dear ajinkya**

straight 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 result

so total lines are = ^{10}C_{2 - }^{4}C_{2} + 1

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11 years ago

4 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? |

3 years ago

3 years ago

25. There are 10 points in a plane, so straight lines can be formed using two at a time. \ Total straight lines = 10C2 = 10 9 2 1 × × = 45 1 But 4 points are collinear. \ Lines using these points = 4 C2 = 4 3 2 1 × × = 6 1 But these 4 points can make a single line. So, Total different lines = 45 – 6 + 1 = 40 1 Now, triangle can be formed using 3 points at a time. So, number of triangles = 10C3 = 10 9 8 321 × × × × = 120 1 Using 4 points taking 3 at a time. No. of triangles = 4 C3 = 4 1 But collinear points can’t make only tirangle. So, Total no. of triangles = 120 – 4 = 116

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