Bipartite Graphs and Matchings · Challenge problem

People $P_1,P_2,P_3$ are each qualified only for openings $\{1,2\}$. People $Q_1,Q_2,Q_3$ are each qualified only for opening $3$. Person $R$ is qualified for openings $\{4,5,6\}$ (seven people total, six openings). What is the maximum number of people who can be placed in distinct openings?