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You are wrong.

so, for my answers, you will have to divide by 13!/(3!3!3!) to get the probabilities

how many ways to arrange EEE? one way. 3! ways if they were all different, but divide by # of identical letters. So yes. Probability just = count them up and divide by total number of possible arrangements.

12!/(3!3!) - 11!/(3!3!) 11!/(3!3!)

you divide by 3! to cover the number of identical arrangements you get by arranging 3 N's.