Select the correct statement(s) about the conversion of alcohols into alkyl halides.

1. A$\mathrm{PBr}{}_3$ converts a primary alcohol into the bromide without carbocation rearrangement because the displacement of the $-\mathrm{OPBr}{}_2$ group is an SN2 reaction.
2. BWith a chiral secondary alcohol, $\mathrm{SOCl}{}_2$ in pyridine gives the chloride with inversion because free chloride attacks the alkyl chlorosulfite from the back.
3. CTreating a chiral secondary alcohol with TsCl in pyridine gives the tosylate with inversion at the carbinol carbon.
4. DConcentrated HCl converts neopentyl alcohol into neopentyl chloride cleanly, without rearrangement.