I was recently asked about these, which appeared in some school worksheets:
(i) You can pay either by cash or cheque.
(ii) You can either pay by cash or cheque.
Sentence (i) was marked ‘formal’, and (ii) as ‘informal’.
Either…or and neither…nor are called ‘correlative conjunctions’: they help us mark out two (and no more) options on offer; i.e. either A or B, neither A nor B.
One thing to note is that A and B should be parallel in structure: if A is a noun, so also should B; if A is a preposition phrase, so also should B.
To illustrate, our options A and B are underlined here: You can choose either to sink or to swim. Note that to sink and to swim are like constituents, i.e. they are both to-infinitives. We do, however, have the option of dropping the second to since it is repeated (i.e. ellipsis) — giving us You can choose either to sink or (to) swim — but some purists would frown upon this. What we can be sure about, however, is that You can either choose to sink or swim is definitely wrong, because either wrongly marks out choose as an option — yet this is probably far more commonly encountered in everyday speech.
Going back to our first two sentences, the clearest way to express the idea is:
(iii) You can pay by either cash or cheque.
However this, for some reason, sounds rather stilted. An improvement would perhaps be:
(iv) You can pay either by cash or by cheque.
Observe that our options, as underlined, are parallel in structure: they’re both preposition phrases (each headed by by).
By contrast, in (i) the options aren’t parallel: by cash is a preposition phrase, while cheque is a noun. Recall, however, that we may argue that the second occurrence of by has been ellipted from by cheque — but recall also that some grammarians would object to this. So, (i) is a little problematic.
Sentence (ii) is even more so, because either is badly placed, marking out pay wrongly as an option.
On balance, I wouldn’t agree that (i) is formal — the honour goes to the rather stilted (iii) and the far more natural (iv). Sentence (ii) is wrong, but perhaps the most natural to speakers.