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All six songs of one artist before the second of another

Question

A 147147-track playlist is shuffled uniformly at random. Four tracks are by DaBaby and six are by Rae Sremmurd. What is the probability that every Rae Sremmurd track plays before the second DaBaby track?

Short answer

1/301/30. Only the relative order of these ten tracks matters. The condition holds exactly when the last three of the ten are all DaBaby tracks, which has probability (43)/(103)=4120=130\binom43/\binom{10}{3}=\tfrac{4}{120}=\tfrac1{30}.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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