Arrange the carbocations in decreasing order of stability: (P) $\mathrm{CH}{}_2=\mathrm{CH}-\mathrm{CH}{}_2{}^{+}$, (Q) $\mathrm{CH}{}_3\mathrm{CH}{}_2\mathrm{CH}{}_2{}^{+}$, (R) $\mathrm{CH}{}_2=\mathrm{CH}{}^{+}$.

The allyl cation is stabilised by resonance, the primary propyl cation only by hyperconjugation and +I. The vinyl cation has its empty orbital in the plane, orthogonal to the pi bond, so it gets no resonance, and the positive charge is on an sp carbon, so it is least stable. Order: P > Q > R.