43% of adults say cashews are their favorite kind of nut. you randomly select 12 adults and ask each to name his or her favorite nut. find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. if convenient, use technology to find the probabilities.

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.