I don't think it's redundant; I think it's wrong. A number doesn't outnumber a population; one population outnumbers another population. If "the number of men and women studying part-time" is (say) 54, then the sentence means: 54 outnumbered those studying full-time. That's not right. The subject of "outnumber" needs to be the thing you're counting, not the result of counting them. Similarly, you would not say: "The number of cats outnumbers the dogs", but rather "The cats outnumber the dogs." I would, however, say "The men and women..." - I think the "the" helps.

Hello Sandy! In A outnumbers B these are unknown entities and it could be singular or plural. But in "the number of men and women studying part-time outnumbered those studying full-time by a significant margin" we know that we are talking about men and women and we are talking about (and comparing) their numbers so the preposition "of" is used to emphasize the relationship between the words "number" and "men and women". So "of" it acts as a clarification. I hope that helps!

Thank you!

I agree. It is redundant, but having this at the beginning of the sentence makes the reader know that you are discussing numbers and quantities later on in the sentence, so it makes it easier to understand.