Distributive pronouns

Consider the following sentences:

Each boy was given a prize.
Either road leads to the railway station.
Neither accusation is true.

Each, either and neither are called distributive pronouns because they refer to persons or things one at a time. Note that a distributive pronoun is always singular and as such it should be followed by a singular noun and verb.

Each new day is different. (NOT Each new days are different.)
Either girl can do that. (NOT Either girls can do that.)
Neither answer is correct. (NOT Neither answers is correct.) (NOT Neither answers are correct.)

Notes

Each of, neither of and either of are followed by plural nouns and singular verbs.

Each of the answers is correct. (NOT Each of the answer is correct.)
Neither of the girls can do that. (NOT Either of the girl can do that.)

Either and neither should be used only in speaking of two persons or things. When more than two persons or things are spoken of, any, no one or none should be used.

None of the three answers is correct. (NOT Neither of the three answers is correct.)
We invited several friends, but none came. (NOT … but neither came.)
You can take any of the three shirts. (NOT You can take either of the three shirts.)

Each

Each can go in different positions.