Can a metal and a nonmetal participate in a combination reaction

Yes

Explanation:

A reaction normally takes place between metals and non metals. The metals acts as the electron donors and the non metals acts as the electron acceptors. This exchange of electrons form bonds such as ionic or covalent.

A good example of a reaction between a metal and non metal is Sodium metal and Chlorine (non metal). They form an ionic bond and the product is Sodium chloride.