A teacher asked $30$ students if they had a school lunch or a packed lunch or if they went home for lunch.  $17$ of the students were boys.  $4$ of the boys had a packed lunch.  $7$ girls had a school lunch.  $3$ of the $5$ students who went home were boys.  Work out the number of students who had a packed lunch. 
Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning 