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Email PHArecruitment@missouri.edu

I would not recommend sending this project and letter to the sororities.

Correct me if I'm wrong, but it is my understanding that PNM's can't take anything into a sorority recruitment event. You should check with your campus Panhellenic.

If recs are not the norm on your campus, don't worry. But I think that if a lot of women are coming through, that recs would be enormously helpful to you.

Personalized cover letters and personal projects are not things that are helpful in the sorority recruitment process. Your recruitment application, grades and alumnae recommendations are the helpful items "on paper" before the sororities get to meet you.
Once you are at a recruitment event, it is up to you and your personality to shine. I think it would be a great idea to talk about the project you are working on at recruitment events, but the sororities will not have time to look over your project.

Also, you have the opportunity to express your interest in person, so your letter of interest is not necessary.

You are correct to assume that sorority recruitment is an interview, but here your application is your "cover letter and resume." And, you have indicated your interest in their organization by coming to their recruitment event and expressing interest to the members.

I think you're better off getting the recs and not submitting your project to the sororities.

Best of luck! For advice about recruitment, check out the hyperlink in my signature.