interview follow up typo

Hi everyone,
I just had an interview and in my follow up email for one of my interviewers, I wrote their names through out the email, but I accidentally wrote the other interviewers name in one of the lines. For example (for simplicities sake, we’ll say the person that i was emailing name is John and the other person is Jane):
“It was great to meet yourself and Jane today,
should I send another email that is corrected. I hope I get the chance to work with you, John, and the rest of the team”
Thank you

 

I think the bigger problem is that it's a bit towards to say "I look forward to working with you" when no offer has yet been extended. It's slightly hubristic. 

 

My bad, I was rushing when I was typing this, but I typically say, “I look forward to potentially working with you” or “I hope I get the chance to work with you”. But in the email I said, I hope to get the chance to work alongside yourself etc etc

 

I mean if that's your personal style, that's fine. I just wouldn't personally write something like that, I usually write something along the lines of thanks for the conversation, learning more about the firm, etc. More nuanced like

 

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