Twelve food units shared among four of ten kids

A babysitter looks after $10$ hungry children and has $12$ identical units of food. She decides that exactly $4$ of the children will be fed and the other $6$ get nothing. In how many ways can she hand out all $12$ units so that each of the chosen $4$ children gets at least one unit?

$34{,}650$. Choose the four fed children in $\binom{10}{4}=210$ ways. Give each of them one unit first, then share the remaining $8$ units freely among the four, which by stars and bars can be done in $\binom{11}{3}=165$ ways. In total $210\cdot165=34{,}650$.