The four isomeric $\mathrm{C}_4 \mathrm{H}_9 \mathrm{OH}$ alcohols are
(i) $\left(\mathrm{CH}_3\right)_3 \mathrm{COH}$
(ii) $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{OH}$
(iii) $\left(\mathrm{CH}_3\right)_2 \mathrm{CHCH}_2 \mathrm{OH}$
(iv) $\mathrm{CH}_3 \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_2 \mathrm{CH}_3$
Synthesize each, using a different reaction from among a reduction, an $\mathrm{S}_{\mathrm{N}} 2$ displacement, a hydration, and a Grignard reaction.
Synthesis of the $3^{\circ}$ isomer, (i), has restrictions: the $\mathrm{S}_{\mathrm{N}} 2$ displacement of a $3^{\circ}$ halide cannot be used because elimination would occur; nor is there any starting material that can be reduced to a $3^{\circ}$ alcohol. Either of the two remaining methods can be used; arbitrarily the Grignard is chosen.
$$
\mathrm{CH}_3 \mathrm{MgI}+\left(\mathrm{CH}_3\right)_2 \mathrm{C}=\mathrm{O} \underset{\text { hydrolysis }}{\stackrel{\text { after }}{\longrightarrow}}\left(\mathrm{CH}_3\right)_3 \mathrm{COH}
$$
The $\mathrm{S}_{\mathrm{N}} 2$ displacement on the corresponding $\mathrm{RX}$ is best for $1^{\circ}$ alcohols such as (ii) and (iii); let us choose (ii) for this synthesis.
$$
\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Cl}+\mathrm{OH}^{-} \stackrel{-\mathrm{Ct}^{-}}{\longrightarrow} \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{OH}
$$
The $1^{\circ}$ alcohol, (iii), and the $2^{\circ}$ alcohol, (iv) can be made by either of the two remaining syntheses. However, the one-step hydration with $\mathrm{H}_3 \mathrm{O}^{+}$to give (iv) is shorter than the two-step hydroboration-oxidation to give (iii).
$$
\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}=\mathrm{CH}_2+\mathrm{H}_2 \mathrm{O}^{+} \stackrel{-\mathrm{H}^{+}}{\longrightarrow} \mathrm{CH}_3 \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_2 \mathrm{CH}_3
$$
Finally, (iii) is made by reducing the corresponding $\mathrm{RCH}=\mathrm{O}$ or $\mathrm{RCOOH}$.
$$
\left(\mathrm{CH}_3\right)_2 \mathrm{CH}_2 \mathrm{COOH} \frac{1 . \mathrm{LiAlH}_4}{2, \mathrm{H}^{+}}-\left(\mathrm{CH}_3\right)_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{OH}
$$