ad 11.
I think that all the possible "combinations" are not 27 but 10, because e.g. tuples (Linux, Windows, Linux) and (Linux, Linux, Windows) are identical. I.e you should count combinations not variations.
All the poss combinations:
LLL, LLW, LLO, LWW, LWO, LOO, WWW, WWO, OWO, OOO
Then you cross out WWW (xterm constraint), and you have 9 combinations, of which 3 are valid for the condition (at least two "Ls"). So 1/3.
No, there are 27 combinations(when you still account for the fact that you can have three windows machines).
You can see it in that way:
machine1: L, machine2: W, machine3: O
machine1: L, machine2: W, machine3: W
The reason why it matters is that you have more ways to have exactly two linux machines:
m1: L, m2: L, m3: O
m1: L, m2: O, m2: L,
etc.
That gives you 2*3 ways of having exactly two linux machines (you have 3 ways of having exactly one non linux machine, and then this machine can be two different things). If you say that LLO is OLL, you would have only 2 ways of having exactly two linux machines.
Comments
Yes, that would make more sense.
ad 11. I think that all the possible "combinations" are not 27 but 10, because e.g. tuples (Linux, Windows, Linux) and (Linux, Linux, Windows) are identical. I.e you should count combinations not variations.
All the poss combinations: LLL, LLW, LLO, LWW, LWO, LOO, WWW, WWO, OWO, OOO
Then you cross out WWW (xterm constraint), and you have 9 combinations, of which 3 are valid for the condition (at least two "Ls"). So 1/3.
Let me know if I got sth wrong :).
No, there are 27 combinations(when you still account for the fact that you can have three windows machines).
You can see it in that way:
machine1: L, machine2: W, machine3: O machine1: L, machine2: W, machine3: W
The reason why it matters is that you have more ways to have exactly two linux machines:
m1: L, m2: L, m3: O
m1: L, m2: O, m2: L,
etc.
That gives you 2*3 ways of having exactly two linux machines (you have 3 ways of having exactly one non linux machine, and then this machine can be two different things). If you say that LLO is OLL, you would have only 2 ways of having exactly two linux machines.
Hope this makes sense.
I see. LLO and LOL are different occurences and must be counted for. Thanks for clarifying!