In World War II, the German's usually used 10 cables on the stecker, only five different rotors were in general use, one reflector was in common use, and the reflector and five rotors were known to...

In World War II, the German's usually used 10 cables on the stecker, only five different rotors were in general use, one reflector was in common use, and the reflector and five rotors were known to the Allies.

a. Under these restrictions, show that there are only about 277  possible Enigma keys.

b. Show that if we ignore the stecker, under these restrictions there are fewer than 230   settings.