Archaeology is largely concerned (but not exclusively) with the study of pre-history — the history of human beings before written records. This is not exactly the line of demarcation, because there are some very old written records, but it does serve to highlight that the mainstay of archaeological work is dealing with material sources as opposed to written ones. So this is a different skill-set than the typical text-based historian.

Anthropology can mean a number of things, ranging from the study of human cultures (of all sorts these days, but historically non-Western ones were the original mainstay) to the study of human evolution (physical anthropology). In the cultural mode it is an ethnographic field about observation of the still living. In the historical mode it is about looking at bones and tools and other material aspects, like archaeology, but also may be looking at more biological materials with tools of genetics.

These three fields obviously intersect and overlap in many places, on many topics. And indeed, they inform each other. But in terms of their disciplines, they distinguish themselves with very different sorts of training. A historian is going to learn about lots of written sources and how to deal with them. An archaeologist is going to spend time analyzing material remains in the field. An anthropologist is either going to be trained in ethnographic practice or something that looks a lot like archaeology mixed with biology. Their topics may overlap, but their methods and questions they ask are going to be different.

As for your specific program, you should inquire with them to find out whether there is something you can do that would demonstrate your competence. If they are only interested in a high school level of science, this is possibly something one can pick up in a remedial fashion later, and they probably have specific things in mind.

Here's my TLDR:

Do you like reading? Study History.

Do you like talking/conversing? Study Anthropology.

Do you like digging? Study Archaeology.

At the level of PhD research, these fields overlap a great deal, of course. Historians borrow from anthropology; archaeologists borrow from historians, it's all one big happy family of interdisciplinarity. But it is strange to me how much these three core principles I mentioned above (reading, talking, digging) actually lie beneath the most sophisticated and nuanced discussions in each field. And the personalities of the people who study them. If you study Anthropology, for instance, you'll read a lot of anthropological theory, much of which is about the boundaries between the subject 'under study' and the person doing the study. In other words, much of this theory is, at core, about a relationship. And their writing is very, very engaging--partially because it is so conversational.

Meanwhile, archaeologists that I know often have a very pragmatic attitude towards what they do. Many work on digs over the summer, of course, but it's more than that: they seem to me far less concerned (as a field) with sophisticated writing or engaging with theory, and more concerned with pragmatic and material things. I have yet to meet an archaeologist swept away by theory. (or who can sweep you away with his/her writing...) They like stuff.

Finally, historians--no matter how much influenced by anthropological theory or how much they try to be interdisciplinary with material things--always come back to sources. Real historians are obsessed about sources--the printed word--that goes far beyond any other field. Interested in a new theory? Great! But do the sources back it up??! Found a 1000-year-old city wall? Great--but what's its significance?? Can you somehow tie it in the historical record?

That's my take, anyway.

I would also question if the way it is divided up makes sense to you all? My BA level opinion is linguistic anthropology should move over to the history department.

I am studying humanities for my diploma in higher education at open uni and finishing with my history degree. We are learning, now in my second year, that anthropology and archeology are both very closely related to humanities and my module is called "voices, texts and material culture"
Our first assignment is to write a biography about an ancient artefact. We have to reflect on both archeology and anthropology to complete this!