Which one is not correct mathematical equation for Dalton's Law of partial pressure? Here p = total pressure of gaseous mixture

$\displaystyle \mathrm{p}_i=\chi_i \mathrm{p}_i^{\mathrm{o}}$, where $\displaystyle \chi_i=$ mole fraction of $\displaystyle i^{\text {th }}$ gas in gaseous mixture $\displaystyle \mathrm{p}_i^{\mathrm{o}}=$ pressure of $\displaystyle i^{\text {th }}$ gas in pure state

$\displaystyle \mathrm{p}=\mathrm{p}_1+\mathrm{p}_2+\mathrm{p}_3$

$\displaystyle \mathrm{p}=\mathrm{n}_1 \frac{\mathrm{RT}}{\mathrm{V}}+\mathrm{n}_2 \frac{\mathrm{RT}}{\mathrm{V}}+\mathrm{n}_3 \frac{\mathrm{RT}}{\mathrm{V}}$

$\displaystyle \mathrm{p}_i=\chi_i \mathrm{p}$, where $\displaystyle \mathrm{p}_i=$ partial pressure of $\displaystyle i^{\text {th }}$ gas $\displaystyle \chi_i=$ mole fraction of $\displaystyle \boldsymbol{i}^{\text {th }}$ gas in gaseous mixture