Six Different Faces
Six fair dice are thrown together. If the six faces shown are all different (so that 1, 2, 3, 4, 5, 6 each appear exactly once), you stop; otherwise you throw all six dice again. What is the expected number of throws? Give an exact value.
Related problems & prerequisites
Worth solving first
- First Heads Wins 3.0/10
- Seven Before Eight 2.0/10
Source: Classic geometric-waiting-time exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.