Learn English – There ‘is’ people or There ‘are’ people

According to MacMillan Dictionary, some can be used as a determiner, followed by an uncountable noun:

I’ll make some coffee.

followed by a plural noun:

She brought me some flowers.

followed by a singular countable noun, to refer to someone or something that is unknown or unspecified:

She married some guy she met on the boat.

All is usually used with plural verb forms, especially when we say "all the X" or "all of the X" where X is plural. "The people" is plural, because there are more than one, so "all of the people" is likewise plural, and the correct answer is A,

All of the people are students.

B is not correct because "a student" is singular, but "all of the people" is plural. "All of the people are a student" - what, all of them are one single student? That doesn't make sense.

C is incorrect because student is a count noun and needs either an article or to be plural: you can "be a student" or you can "be students", but you can't just "be student".