Calvin visits McDonalds

From the given information , Calvin orders 10 burgers and there are 4 kinds of burgers.So we use the technique of stars and bars where stars are the 10 burgers and 3 bars which classify the 4 kinds of burgers. Thus total symbols are 13 and the total ways Calvin can order are : $\Large{13\choose 3} = 286$ .

Some other approach: Let the types of burgers be $B_1,B_2,B_3,B_4$ .

Say $x_1$ number of burgers are of $B_1$ kind.Say $x_2$ number of burgers are of $B_2$ kind.Say $x_3$ number of burgers are of $B_3$ kind.Say $x_4$ number of burgers are of $B_4$ kind.Then we have

$\Large\displaystyle\sum_{i=1}^4 x_i =10 \ where \ \forall i \ x_i \geq 0$

And for this there are $286$ solutions possible using stars and bars.

A+B+C+D=10 (10+4-1)c(4-1)=286