1.

i) If 7 points of 12 are in a straight line, then find the number of traingles that can be formed by selecting any 3 of them

ii)Under the same situation , find the number of straight lines that can be formed by jining these lines

1. A triangle is formed by joining any three points which are not collinear

in first part no. of triangles formed =** no. of triangle formed by 12 points-no. of triangles formed by 7 points**

=^{12}C_{3}-^{7}C_{3}

=220-35=**185**

2.A straight line is formed by joining any two points

no. og straight lines=**straight lines formed by 12 poins-straight lines formed by 7 points+1 ** ** (1 is added because the 7 points which are on a straight line also represent a straight line)**

so no. of lines=^{1}^{2}C_{2}-^{7}C_{2}+1

=66-21+1=**46**

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