Figurine Figuring
A Jane Street holiday puzzle: 78 figurines (12 drummers, 11 pipers, 10 lords, … 1 partridge) are shuffled and drawn without replacement until the partridge emerges. What is the expected value of the maximum count of any one figurine type drawn?
Monte Carlo simulation gives an expected value of 6.87 (to two decimal places). The full Python simulation, which runs 10 million trials using a Counter for per-type counts, is in the PDF.