Never Behind
Alice receives 6 votes and Bob receives 4. The 10 ballots are counted one at a time, and a counting order is recorded as a sequence of six A's and four B's (so there are C(10, 4) = 210 possible orders). In how many of these orders does Alice's running total never fall below Bob's (ties are allowed)? Give an integer.
Related problems & prerequisites
Worth solving first
- Grid Paths 4.0/10
- The Hurried King 4.0/10
- Paths Below the Diagonal 3.0/10
Source: Weak form of Bertrand's ballot problem, solved by the reflection principle. Statement written for AxiomIQ.