The correct statement$(s)$ about the compound $\mathrm{H}_3 \mathrm{C}(\mathrm{HO}) \mathrm{HC}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH}) \mathrm{CH}_3(\mathbf{X})$ is(are)

$(A)$ The total number of stereoisomers possible for ${X}$ is $6$

$(B)$ The total number of diastereomers possible for ${X}$ is $3$

$(C)$ If the stereochemistry about the double bond in ${X}$ is trans, the number of enantiomers possible for ${X}$ is $4$

$(D)$ If the stereochemistry about the double bond in ${X}$ is cis, the number of enantiomers possible for ${X}$ is $2$

  • [IIT 2009]
  • A

    $(A, D)$

  • B

    $(A, B)$

  • C

    $(A, C)$.

  • D

    $(B, D)$

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  • [AIIMS 2016]

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