Set of pairs of options that could be wrong/right One has a list of n options out of which 2 are incorrect, and guesses can be made by picking a pair of options. After picking a pair as a guess, it is either valid, in which case both of the pair's options are incorrect, or not, in which case one or both are a correct option.
How would making a invalid guess change the probability of other pairs being valid?

You have $n(n-1)/2$ possible pairs of which $2(n-1)-1$ pairs are incorrect hence the probability to pick an incorrect pair is $(4(n-1)-2)/(n(n-1))$.
Will making an invalid guess you gain information on where is, at least one, of the incorrect options. Thus the probability of getting an incorrect pair decrease. You have now $n(n-1)/2-1$ possible pairs (all the pair minus the one you picked) and $2(n-1)-2$ incorrect ones. hence the probability is now $2(n-2)/(n(n-1)/2-1)$.
