Suppose $N$ experimental units are randomly assigned to treatment or control by tossing a coin. A unit is assigned to treatment if the coin toss comes up heads. Assume that the probability of tossing a head is $p$.

a. If $p=1 / 3$, then are all treatment assignments equally likely?

b. Identify treatment assignments that do not allow estimating the causal effect of treatment versus control. Explicitly state the treatment assignment vectors for the identified assignments. How many of them are there?