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Here are 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?



TCS-latest-placement-paper-Here-is-15-dots-if-you

A440/455

B434/455

C449/455

D438/455

ENone of these

Answer: Option (Login/Signup)

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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)}  ] 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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