Fragen über die Beispielsätze mit, und die Definition und Benutzung von "Varieties"

A: "a variety of" (many types 様々な) and "a number of" (many　数多い) are set phrases. Just think of it as an exception to normal grammar rules.

"A type of"（一種） means a single type among many things. "Types" is the plural form and refers to many types, not one single type.