Will a 3.8 GPA and 1 F with an explanation on transcript allow me to get into graduate school? I am currently in my junior year, studying abroad in another country. The advisor at this school told me that I was enrolled in 5 businesses classes. I had asked her to drop one of them because I didn't need it and she said okay I will drop this course for you and you have 12 credits. I left her office and went on with my day and I came to find out later that she had not dropped my course and that I am still enrolled in 5 classes. The way the school works here is that you are unable to add/drop once that period is over. 

Upset and frustrated, I went to her office and she said she can't remember what had happened because she has too many students. She had told me that I can either take the course or fail it and it won't affect my GPA. But on my transcripts it will say grade not available aka "F." I normally take 4 classes at home and I do want to enjoy my time here, so I don't know if I should take the "F" and explain what had happened to graduate school admissions office or just suffer and take the class that I don't need toward my major. It will not affect my GPA whatsoever if I were to take the F it will just be on my transcripts.

I trusted my advisor that she dropped my course, had I known that she wouldn't do it I would've done it myself. I do understand that I am at fault to for not checking it right after she'd done it, but by the time I found out it was too late. Thoughts?
Don't overthink things -- these things happen, and the people who make the selection among graduate students know this as well. If the rest of your grades are good and you have a good explanation, then that's all that's necessary.