Explain why "dial combinations" are not mathematical combinations expressed by the equation Subscript n Baseline Upper C Subscript x Baseline equals StartFraction n exclamation mark Over x exclamation mark left parenthesis n minus x right parenthesis exclamation mark EndFraction

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.