Runs in a Row
Six items of type A and four of type B are arranged in a row, all $\binom{10}4=210$ arrangements being equally likely (the null hypothesis of the runs test for randomness). A run is a maximal block of consecutive identical letters, so AABBBAAAAB has 4 runs. What is the probability of observing at most 3 runs? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Seven of Eight Recovered 2.0/10
Source: Wald-Wolfowitz runs test (1940). Numbers written for AxiomIQ. Statement written for AxiomIQ.