An election, with a twins twist
A city council consists of 10 members, from whom will be selected 4 officers: President, Vice-President, Secretary, and Ombudsman. But two of the members of the council are identical twins, and no one can tell them apart! If the twins are "interchangeable", whether elected to an office or not, in how many ways can the positions be filled ?
(Historical note: In 2006-2007, the identical twin Kaczynski brothers were President and Prime Minister of Poland.)