What is the combinatorial reasoning for the $n$ factor in $n \times n! / (b!(n - b)!)$?
Part of the state of the world is the location of the agent. Since there are $n$ cells, this variable has $n$ possible values, producing the factor of $n$.
Actually, there may be a mistake in Russell and Norvig's formula. After we have chosen the location of the agent, there are only $n - 1$ possible locations for the $b$ boxes, giving us $(n - 1)! / (b! (n - b - 1)!)$ choices for where to put all of the boxes. So, the number of states is $n \times (n - 1)!/(b!(n - b - 1)!)$, which simplifies to $n! / (b! (n - b - 1)!)$. (This is the trinomial coefficient $n \choose 1, b$.)