In the elementary steps of a reaction, why do we assume that the coefficients of a reactant correspond to its order?

Recently, I was taught that the coefficients of the reactants in an elementary step of a reaction indicates that reactant's order. Why is this the case? I thought that the order of a reactant was not related to its coefficient.


For example, in the following termolecular reaction mechanism


$$\ce{A + 2B -> C + 2D}$$


the rate law is $k[\ce{A}][\ce{B}]^2$. Why is this the case?


**EDIT:** Also, for equilibrium reactions, do we always assume the coefficients of the reactants to provide the order for those reactants? What about for equilibrium reactions involving multiple steps?




If a reaction has just one step, it's named an *elementary reaction*. In this reaction all of reactant directly participate on reaction and effectively collide with each other. So, the order of reaction corresponds to its coefficient, but if a reaction is not a elementary reaction, there isn't any reason for colliding all reactants with each other. For example, consider the following overall reaction:


$$\ce{A + B + D -> F}$$


Assume the corresponding mechanism is constituted of two elementary reactions:


$$\ce{A + B -> C}$$
$$\ce{C + D -> F}$$


As shown above, there is no need to collide A with D or A with C ... Then, in these type of reactions coefficients are not corresponded to order of reaction . 


 9