[asy]
size(140);
import geometry;
dot((0,0));label("(0,0)",(0,0),SW);
dot((4,3));
dot((5,4));label("(5,4)",(5,4),NE);
draw((0,0)--(7,0), EndArrow);
draw((0,0)--(0,6), EndArrow);
add(grid(5,4));
[/asy]
A leprechaun wishes to travel from the origin to a pot of gold located at the coordinate point (5,4). If she can only move upwards and rightwards along the unit grid, must pass a checkpoint at (1,2), and must avoid an evil thief at (4,3), how many distinct paths can she take?<spanclass=′latex−bold′>(A)</span>7<spanclass=′latex−bold′>(B)</span>15<spanclass=′latex−bold′>(C)</span>21<spanclass=′latex−bold′>(D)</span>45<spanclass=′latex−bold′>(E)</span>126