The initial rates of reaction $3\mathrm{A}+2\mathrm{B}+\mathrm{C}⟶$Products, at different initial concentrations are given below:
 

Initial rate Ms-1	$[\mathbf{A}{]}_0,\mathbf{M}$	$[\mathrm{B}{]}_0,\mathbf{M}$	$[\mathrm{C}{]}_0,\mathbf{M}$
5.0 x 10-3	0.010	0.005	0.010
5.0 x 10-3	0.010	0.005	0.015
1.0 x 10-2	0.010	0.010	0.010
1.25 x 10-3	0,005	0,005	0.010

The order with respect to the reactants, A, B and C are respectively 

From $1^{\text{st }}\text{ and }{2}^{\text{nd }}$sets of data - no change in rate is observed with the change in concentration of ‘C’ So the order with respect to ‘C’ is zero. From 1^st and 4^st sets of data Dividing eq. (4) by eq. (1) 
$$\begin{gathered} \frac{1.25\times {10}^{-3}}{5.0\times {10}^{-3}}={\left[\frac{0.005}{0.010}\right]}^{\mathrm{x}} \\ \text{ or }0.25=(0.5{)}^{\mathrm{x}}\text{ or }(0.5{)}^2=(0.5{)}^{\mathrm{x}} \\ \therefore \mathrm{x}=2 \\ \text{ The order with respect to ' }\mathrm{A}\text{ ' is }2\text{ from the }{1}^{\text{st }}\text{ and }{3}^{\text{rd }} \\ \mathrm{sets} \mathrm{of} \mathrm{data} \mathrm{dividing} \mathrm{eq}. (1) \mathrm{by} \mathrm{eq}. (3) \\ \frac{5.0\times {10}^{-3}}{1.0\times {10}^{-2}}={\left[\frac{0.005}{0.010}\right]}^{\mathrm{y}} \\ \text{ or }(0.5{)}^1=(0.5{)}^{\mathrm{y}}\Rightarrow \mathrm{y}=1 \\ \mathrm{The} \mathrm{order} \mathrm{with} \mathrm{respect} \mathrm{to} ‘\mathrm{B}’ \mathrm{is} 1 \\ \mathrm{So} \mathrm{the} \mathrm{order} \mathrm{with} \mathrm{respective} \mathrm{the} \mathrm{reactants} \mathrm{A}, \mathrm{B} \mathrm{and} \mathrm{C} \mathrm{is} 2, 1 \mathrm{andO}. \end{gathered}$$