8. How many anagrams, even without meaning, are there of the word ``STUDIARE''? In how many of these anagrams can the word ``ARTE'' be read consecutively, as for example in ``SUARTEDI''?
How many anagrams, even without meaning, are there of the word ``VACANZA''? ``Mathematics knows no races or geographical boundaries; for mathematics, the cultural world is a single nation''
\footnotetext{Maximum duration of the exam: 6 hours. The use of scientific or graphical calculators is permitted provided they are not equipped with symbolic algebraic processing capability and do not have Internet connectivity. The use of a bilingual dictionary (Italian–language of the country of origin) is permitted for candidates whose native language is not Italian. It is not permitted to leave the Institute before 3 hours have elapsed from the distribution of the exam. }