The different solutions are right.
I simply wished so as to add right here the “great distance” of doing it.
I imply all of the doable instances.
Case 1.
Car Goat Goat
Case 1.1.
You select door 1.
Monty opens| change | do not change
2 | Lose | Win
3 | Lose | Win
Case 1.2.
You select door 2.
Monty opens| change | do not change
3 | Win | Lose
Case 1.3.
You select door 3.
Monty opens| change | do not change
2 | Win | Lose
Case 2.
Goat Car Goat
Case 2.1.
You select door 1.
Monty opens| change | do not change
3 | Win | Lose
Case 2.2.
You select door 2.
Monty opens| change | do not change
1 | Lose | Win
3 | Lose | Win
Case 2.3.
You select door 3.
Monty opens| change | do not change
1 | Win | Lose
Case 3.
Goat Goat Car
Case 2.1.
You select door 1.
Monty opens| change | do not change
2 | Win | Lose
Case 2.2.
You select door 2.
Monty opens| change | do not change
1 | Win | Lose
Case 2.3.
You select door 3.
Monty opens| change | do not change
1 | Lose | Win
2 | Lose | Win
