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Question

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

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Solution

Integral points that line interior are (x,y) when x>o,y>o but x+y<41
that means find positive integral solutions of equation x+y<41
x>0,y>0 so at least x=1,y=1
So that means
x+y39
So that x,y can take 0..........39, any value
Total points = (No. of nonintergral solutions of x+y=0,x+y=1,....x+y=39).
=1C2+2C1+3C1
=1+2+3....40
=40(41)2=820.

1072758_1156369_ans_38fd1a13cf714071b9f3261c211ed009.png

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