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Here are 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?
A440/455
B434/455
C449/455
D438/455
ENone of these
Show Explanation
total possibilities=4c3=455
now we have to find the number of dots that do not make a triangle;
3 dots from each row are collinear.So they will not form a triangle.thus total dots from each row possible=3*5c3=30
Each column is collinear.So 5 straight lines formed.
now consider the dots [ { (1,1),(2,2),(3,3)} , {(1,2),(2,3),(3,4)} ,{ (1,3),(2,4).(3,5)}Â ] each set here does not make a triangle as they are collinear.Same goes for other three points {(1,3),(2,2),(3,1)} {(1,4),(2,3),(3,2)},{(1,5),(2,4),(3,3)}.So 3+3=6 straight lines that does not make a triangle.Also each dots from diagonals are collinear and thus does not make a triangle.So again 2 straight lines formed.
So total dots that does not make a triangle are=30+5+6+2=43
So no of triangles formed are=455-43=412
probability=412/455
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