Bipartite Graphs and Matchings · Medium problem

Four interns $1,2,3,4$ need desks: $1$, $2$, and $3$ can each use desk $a$ or desk $b$ only, while $4$ can use desk $c$ or desk $d$. At first glance every PAIR of interns seems to share enough desks (any two of $1,2,3$ have both $a$ and $b$ between them). Does a desk assignment exist that seats all four interns at distinct desks? If not, what is the maximum number that can be seated?