Identify the correct statements about the compound: 

  $$\begin{gathered} {\mathrm{CH}}_3\left(\mathrm{OH}\right)\mathrm{HC}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}\left(\mathrm{OH}\right){\mathrm{CH}}_3 \\ \left(\mathrm{Y}\right) \end{gathered}$$

(a) If stereochemistry around the double bond in $\mathrm{Y}$ is cis, the number of enantiomers possible for $\mathrm{Y}$ is $2$.

(b) There are $4$ meso stereoisomers possible for $\mathrm{Y}$.

(c) Total number of stereoisomers possible for $\mathrm{Y}$ is $4$.

(d) All stereoisomers of $\mathrm{Y}$ are optically active.