Team assignments with two marketing refusals

A startup's $12$ employees must be split into a software team of $3$, a content team of $4$ and a marketing team of $5$. Two particular employees, $A$ and $B$, refuse to be on the marketing team. In how many ways can everyone be assigned?

$8820$. Fill marketing first from the $10$ eligible people in $\binom{10}{5}=252$ ways; then pick software from the $7$ who remain in $\binom73=35$ ways, and the last $4$ form the content team. So $252\cdot35=8820$.