Carol constructed a cube and marked each face with a number. She marked the faces with the numbers 1, 2, 2, 3, 3, and 4. If she rolls the cube twice, what is the probability that the sum of the numbers will be exactly 7?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.