Practice Counting Problems

  1. The number of (n,p,q) machines with no reflecting branches.
  2. The number of (n,p,q) machines in which each state has a reflecting branch.
  3. The number of (n,p,q) machines in which exactly 3 states have reflecting branches. Assume n > 3.
  4. The number of (n,p,q) machines with at least one reflecting branch.
  5. The number of (n,p,q) machines, n > 2, p > 2, with no reflecting branches and such that each state has exactly 2 diverging branches.