How many possible Enigma machine settings? I'm trying to calculate the amount of settings the enigma machine has. I have found several sites regarding this topic, but it seems like there are two answers to my question. The first answer is 158,962,555,217,826,360,000 and the second is 107,458,687,327,250,619,360,000. Where the difference is that in the second answer, it has been taken into account that the notched rings on the enigma could be set as well, giving 26 * 26 = 676 more settings than the first answer. 

But which answer is the right one, and why? How many possible different Enigma machine settings are there and how can one determine this number?
Depends on the exact model. Wikipedia is your friend: "Combining three rotors from a set of five, the rotor settings with 26 positions, and the plugboard with ten pairs of letters connected, the military Enigma has 158,962,555,217,826,360,000 (nearly 159 quintillion) different settings."



More in detail: if you consider an Enigma with 3 rotors out of 5 rotors of model known to the cryptanalyst, and a plugboard with 10 wires


the 3 rotors out of 5 can be ordered in ${5!\over(5-3)!}=60$ ways.
for each rotor, the relative position of the wiring to the rest of the rotor can be set to 26 positions; for $26^3=17,576$ combinations.
each of the 20 extremities of the 10 wires can be plugged into any of 26 positions not otherwise occupied, with the two extremities of a given wire equivalent, as well as the 10 wires themselves; for
${26!\over(26-20)!\cdot2^{10}\cdot10!}=150,738,274,937,250$ combinations.


There are thus
$${5!\over(5-3)!}\cdot26^3\cdot{26!\over(26-20)!\cdot2^{10}\cdot10!}=158,962,555,217,826,360,000$$
possible settings, for a definition of that not including the initial rotor position, even though that's not initially known to the cryptanalyst.