Choose the correct variant: there are 584 students at the department: а) five and hundred eighty-four. в) five hundred and eighty-four. с) five eighty-four hundred. d) five hundred eighty fourth. e) five hundred and eighty four. объясните, , почему. я вообще этого не понимаю

D or E if we are talking about american english 'and' tends to be removed in it. It makes sense because 'and' can be seen as a synonym of plus in the mathematical sense. It is more used when you are listing or adding up numbers.  However, in UK 'and' is always used, so it literally depends on what you are teacher is looking for.