Rain vs. rains

[rumi.]

English Error, Elementary Level

ESL/EFL Test #15 "The Months of the Year", question 7

January is usually a very cold month with plenty of rains and sometimes snow. February is the shortest month — usually containing only 28 days.

(a) is
(b) rains
(c) the shortest

English Error, Elementary Level

ESL/EFL Test #15 "The Months of the Year", answer 7

January is usually a very cold month with plenty of rain and sometimes snow. February is the shortest month — usually containing only 28 days.

Correct entry: rain
The error was: (b) rains
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I do not understand the sentence, I mean I don't understand what is wrong!!
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Rumi

[Conchita]

[Markbjorndal]

I understand the problem here, but what I do not understand is when and why do you use an "s" after rain or play and what is the meaning of this (in other words, why do you use it?)