Arrange the compounds of each set in order of reactivity towards $S_{N}2$ displacement:
$(i)$ $2-Bromo-2-methylbutane$,$1-Bromopentane$,$2-Bromopentane$
$(ii)$ $1-Bromo-3-methylbutane$,$2-Bromo-2-methylbutane$,$2-Bromo-3-methylbutane$
$(iii)$ $1-Bromobutane$,$1-Bromo-2,2-dimethylpropane$,$1-Bromo-2-methylbutane$,$1-Bromo-3-methylbutane$.

(N/A) $(i)$ $1-Bromopentane$ $(1^{\circ})$,$2-Bromopentane$ $(2^{\circ})$,$2-Bromo-2-methylbutane$ $(3^{\circ})$. The $S_{N}2$ reactivity decreases as steric hindrance increases. The order is: $2-Bromo-2-methylbutane < 2-Bromopentane < 1-Bromopentane$.
$(ii)$ $1-Bromo-3-methylbutane$ $(1^{\circ})$,$2-Bromo-3-methylbutane$ $(2^{\circ})$,$2-Bromo-2-methylbutane$ $(3^{\circ})$. The order of reactivity is: $2-Bromo-2-methylbutane < 2-Bromo-3-methylbutane < 1-Bromo-3-methylbutane$.
$(iii)$ All are $1^{\circ}$ alkyl halides. Reactivity decreases as branching near the reaction site increases. The order is: $1-Bromo-2,2-dimethylpropane < 1-Bromo-2-methylbutane < 1-Bromo-3-methylbutane < 1-Bromobutane$.