Assume no more than 5 questions are used and every question asked is answered correctly by one of the competitors. How many different ways can the final round play out such that Competitor A wins the round? (Example I: Competitor A could get the first 3 questions correct (AAA), Example II: Competitor B could get only the second question correct (ABAA).)

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Assume no more than 5 questions are used and every question asked is answered correctly by one of the competitors. How many different ways can the final round play out such that Competitor A wins the round? (Example I: Competitor A could get the first 3 questions correct (AAA), Example II: Competitor B could get only the second question correct (ABAA).)
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The final round can play out such as ABA BAA AAB AAA

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