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what is the probability of getting a sum of 5 before 7 when 3 dice are thrown?

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(2*6!+21*6!)/(14*7!+14*13!) find remainder? Juliet has attempted problems on Brilliant and solved of them correctly. Her friend Romeo has just joined Brilliant, and has attempted problems and solved correctly. From now on, Juliet and Romeo will attempt all the same new problems. Find the minimum number of problems they must attempt such that it is possible that Romeo's ratio of correct solutions to attempted problems will be strictly greater than Juliet's.