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(A) The stability of dimethylcyclohexane isomers depends on the number of equatorial methyl groups and steric interactions.$1$. Structure $(I)$ is $tr

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$I > II \approx III > IV$

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(A) The stability of dimethylcyclohexane isomers depends on the number of equatorial methyl groups and steric interactions.$1$. Structure $(I)$ is $trans-1,3-$dimethylcyclohexane in the diequatorial conformation,which is the most stable.$2$. Structures $(II)$ and $(III)$ are $cis-1,3-$dimethylcyclohexane (one equatorial,one axial) and $trans-1,4-$dimethylcyclohexane (one equatorial,one axial) respectively. These have similar stability due to one axial methyl group.$3$. Structure $(IV)$ is $cis-1,4-$dimethylcyclohexane in the diaxial conformation,which is the least stable due to severe $1,3-$diaxial interactions.Therefore,the decreasing order of stability is $I > II \approx III > IV$.

Arrange the following molecules in the correct order of stability (decreasing order):

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