22. There are n triangles of positive area that have one vertex A(0,0) and the other two vertices whose coordinares are drawn independently with replacement from the set {0,1,2,3,4} e.g. (1,2), (0,1), (2,2) etc. Find the value of n.
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4 Answers
62Awesome question [1]
Hint: First find the number of vertices...
then the number of triangles.
Then substract those made by points that lie on a straight line
1That means
No of vertices = 55
No. of triangles = 55C
2
Should we manually count all those points which lie on a strt line????????
62no of vertices is not 55 but 52=25
out of which one is the origin..
No of triangles with one point at origin is 24C2
now try
1no. of points lying on a strt line are 4 on x - axis 4 on y- axis 4 on x = y and 2 each
on y = 2x and x = 2y
So , 24 c 2 - ( 4c2 + 4c2 + 4c2 + 2c2 + 2c2 ) = 256