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Question

The number of points, having both co-ordinates as integers, that lie in the interior of the triangles with vertices (0,0),(0,41) and (41,0) is

A
901
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B
861
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C
820
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D
780
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Solution

The correct option is B 780
Required point (x,y) is such that it satisfies
x+y<41
and x>0 and y>0
Number of positive integral solutions of the equation x+y+k=41 will be number of integral coordinates in the bounder region.
the total number of integral coordinates,
=411C31=40C2=40!2!38!=40×392=20×39=780

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