$f(x)=a{x}^4+b{x}^3+c{x}^2+dx+e$, where $a,b,c,d,$ and $e$ are real numbers.

Suppose $f(x)=1$ has $p$ distinct real solutions, $f(x)=2$ has $q$ distinct real solutions, $f(x)=3$ has $r$ distinct real solutions, and $f(x)=4$ has $s$ distinct real solutions.

Which one of the following is not possible?