MathDB

In the

6\times4

grid shown,

12

of the

24

squares are to be shaded so that there are two shaded squares in each row and three shaded squares in each column. Let

N

be the number of shadings with this property. Find the remainder when

N

is divided by

1000

. [asy]size(100); defaultpen(linewidth(0.7)); int i; for(i=0; i<5; ++i) { draw((i,0)--(i,6)); } for(i=0; i<7; ++i) { draw((0,i)--(4,i)); }[/asy]

Problem Statement