Recommendation letters for assistant professor position (computer science and statistics) I am applying for (research) assistant professor positions in the computer science and statistics areas. I have seen advice on having at least one recommendation letter outside of my graduate school institution. I have two letters from inside my graduate school institution.

One letter is from my major professor, who can comment on my ability to obtain grants and conduct research. The other letter is from a professor who can comment on my ability to teach and conduct research.

I am currently deciding about my third letter, and have two options in mind. One idea is my manager at a software company from my summer internship in 2016. She can comment on my ability to get work done, work with team members, demonstrate software development skills, and make connections (she told me I was persistent in asking for the internship position). The other idea is a professor emeritus who I worked with back in 2009 during a postbac position. He is now in his early 80s but still publishes research. He was the founding chair of an academic department (not directly related to what I do now though within the sciences and maths), won several prestigious awards, and served most of his time in academia. He can comment on my research abilities and initiative (he was impressed that I developed my own research ideas to fruition during my postbac). He has written a recommendation letter for me back in 2012 to apply for graduate school.

I would be grateful to hear opinions on this topic. Do you think either of these third options appropriate? Is one more favorable than the other? Most applications require exactly 3 letters, but some allow 4 letters. Hence, I can include both for some applications. Thank you for sharing any of your wisdom!
Well, given that you are applying for a professorship position it makes much more sense the second third option. The recruiters do look for external recommendations, but external recommendations in the same area are more valuable as they give more interesting information on the candidate for that role.
However, if i may, i would suggest you to have the first recommendation for your ability to get grants, the second one for your ability to teach and the third one for your ability to research. In this way, the recommendations will be covering all the aspects of the job, without overlapping each other and without overwhelming the recruiters.
I hope my suggestions will help you.