$PGF_{2\alpha}$ is a prostaglandin, a group of compounds that are responsible for inflammation (Section 19.6). (a) How many tetrahedral stereogenic centers does $PGF_{2\alpha}$ contain? (b) How many double bonds can exist as cis and trans isomers? (c) Considering both double bonds and tetrahedral stereogenic centers, what is the maximum number of stereoisomers that can exist for $PGF_{2\alpha}$?