Triangle ABC will be constructed in a xy-plane according to the following conditions: Angle ABC is 90 degrees, and AB is parallel to the y-axis; for each of points A, B and C, both the x-coordinate and the y-coordinate must be integers; the range of possible x-coordinates is 0=<x=<5 and the range of possible y-coordinates is -4=<y=<6. Any two triangles with non-identical vertices are considered different. Given these constraints, how many different triangles could be constructed? Pick.
A) 50 B) 66 C) 2500 D) 3300 E) 4356
Since give that 0=&lt;x=&lt;5 and -4=&lt;y=&lt;6 then we have a rectangle with dimensions 6*11 (6 horizontal and 11 vertical dots). AB is parallel to y-axis, BC is parallel to x-axis and the right angle is at B.   Choose the (x,y) coordinates for vertex B: 6C1*11C1;   Choose the x coordinate for vertex C (as y coordinate is fixed by B): 5C1, (6-1=5 as 1 horizontal dot is already occupied by B);   Choose the y coordinate for vertex A (as x coordinate is fixed by B): 10C1, (11-1=10 as 1 vertical dot is already occupied by B).   6C1*11C1*5C1*10C1=3,300.   Answer: 3300
<result>D</result>
Triangle ABC will be constructed in a xy-plane according to the following conditions: Angle ABC is 90 degrees, and AB is parallel to the y-axis; for each of points A, B and C, both the x-coordinate and the y-coordinate must be integers; the range of possible x-coordinates is 0=<x=<5 and the range of possible y-coordinates is -4=<y=<6. Any two triangles with non-identical vertices are considered different. Given these constraints, how many different triangles could be constructed?