WeBWorK using host: https://webwork-dev.aimath.org, format: simple, seed: 96, course: anonymous

How many functions $f: \{1,2,3,4,5\} \to \{a,b,c,d,e\}$ are there satisfying:

$f$ is surjective, but $f(1) \ne a\text{,}$ $f(2) \ne b\text{,}$ $f(3) \ne c\text{,}$ $f(4) \ne d$ and $f(5) \ne e\text{?}$