If the coefficient of x and x² in the expansion of $(1+\mathrm{x}{)}^{\mathrm{p}}(1-\mathrm{x}{)}^{\mathrm{q}},\mathrm{p},\mathrm{q}\le 15$ are –3 and –5 respectively, then the coefficient of x³ is equal to

$$\begin{gathered} \text{ Since coefficient of }\mathrm{x}\text{ is }-3 \\ \begin{array}{r}{\Rightarrow }^p{\mathrm{C}}_1{-}^9{\mathrm{C}}_1=-3\\ \Rightarrow \mathrm{p}-\mathrm{q}=-3\\ \text{ Comparing coefficients of }{\mathrm{x}}^2\\ \begin{array}{r}{-}^{\mathrm{p}}{{\mathrm{C}}_1}^{\mathrm{q}}{\mathrm{C}}_1{+}^{\mathrm{p}}{\mathrm{C}}_2{+}^{\mathrm{q}}{\mathrm{C}}_2=-5\\ -\mathrm{pq}+\frac{\mathrm{p}(\mathrm{p}-1)}{2}+\frac{\mathrm{q}(\mathrm{q}-1)}{2}=-5\\ p=8,q=11\\ \text{ Coefficient of }{\mathrm{x}}^3\text{ is }\\ \begin{array}{r}{-}^q{\mathrm{C}}_3{+}^p{\mathrm{C}}_3{+}^{\mathrm{P}}{\mathrm{C}}_1^{\mathrm{q}}{\mathrm{C}}_2{-}^{\mathrm{p}}{\mathrm{C}}_2^{\mathrm{q}}{\mathrm{C}}_1\\ ={-}^{11}{\mathrm{C}}_3{+}^8{\mathrm{C}}_3{+}^8{{\mathrm{C}}_1}^{11}{\mathrm{C}}_2{-}^8{{\mathrm{C}}_2}^{11}{\mathrm{C}}_1\\ =23\end{array}\end{array}\end{array} \end{gathered}$$