Monsters and Munchkins

$3$ monsters and $3$ munchkins are on the left bank of the river and need to cross to the right bank using a boat. This boat has a capacity of $3$ creatures, and because the river currents are strong, at least $2$ creatures are needed to row the boat for any river crossing. If the monsters ever outnumber the munchkins on one of the river banks, they will eat them.

a$)$ Draw a complete transition diagram showing all the possible sequences of river crossings under these constraints. Your transition diagram should include all the crossings, even the ones that lead to dead ends for some of the munchkins. States should not be repeated. $($note that you can use a power notation shorthand to describe the number of creatures: e$.$g$.$u$3$o$3$

to refer to $3$ munchkins and $3$ monsters.$)$

b$)$ Exactly how many different sequences of river crossing will get the six creatures safely across the river without anybody being eaten?