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There are 'm' points on a straight line AB and 'n' points on the line AC none of them being the point A. Triangles are formed with these points as vertices, when (i)A is excluded (ii) A is included. The ratio of no of triangles in the 2 cases is ?

There are 'm' points on a straight line AB and 'n' points on the line AC none of them being the point A. Triangles are formed with these points as vertices, when


 (i)A is excluded (ii) A is included. The ratio of no of triangles in the 2 cases is ? 

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear jee king

case 1   A is excluded

total ways =m+nC3

but triangle can't be formebd joining the 3 points which are in straight line so

total number of possible triangle=m+nC3  -mC3  -nC3

 

Case 2 A is included

otal ways =m+n+1C3

but triangle can't be formebd joining the 3 points which are in straight line so

total number of possible triangle=m+n+1C3  -m+1C3  -n+1C3


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Badiuddin

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