Why does the dimethylaniline couple with the diazonium salt at the para position of the ring?

Explanation:

In the coupling reaction of the dimethylaniline and diazonium salt, both electronic and steric factors play a very important role. The resonance structures of dimethylaniline favor electrophilic attack at both the ortho and the para positions. But on the other hand, diazonium coupling produces the majority of  the para product because the steric factor plays role here in this reaction.

The bulky dimethylamino groups on the dimethylaniline make it difficult for electrophile to approach ortho position and also, diazonium ion is relatively large. The two steric factors reduce amount of the ortho isomer and para isomer predominates.