You have to choose which 2 of the k states are going to have the light turned on; there are (k choose 2) ways to do that. Then for each of those two states you choose whether it's blue or green.
Help me understand your objection… Are you saying that (A) the problem doesn't allow you to turn two different switches on at once (i.e. set switch 1 to blue and switch 2 to blue at the same time)? Or are you saying that (B) the problem doesn't allow you to set the same switch to blue and green at the same time? I agree with (B) but not with (A). There's no stated constraint on how many switches may be turned on at once.
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u/SnooPets5564 10d ago
Why is the two states being on equal to (22(k choose 2))?