Marinada '25

[lang=hr] Simeon na rukama ima \textbf{rukavice}, \textbf{prstenje} i \textbf{lak za nokte}. Na nogama ima \textbf{službene MNM tenisice}, \textbf{photomath čarape}, \textbf{lak za nokte}, \textbf{gljivice}, a sve to mu je još obavijeno \textbf{plastičnim vrećicama} koje je ukrao na MNM-ov račun. Simeon mora također obavljati svoje administrativne MNM poslove i pripremati se za ispite, stoga slučajno odabire što će sljedeće skinuti sa sebe. Simeon može skidati stvari s ruku i nogu samo na smislen način. Ne može skinuti lak i prstenje s ruku dok ne skine rukavice, ali nakon što skine rukavice može proizvoljno skinuti ili lak ili prstenje. Za nogu mora prvo skinuti vrećicu, pa tenisicu, pa čarapu, pa lak za nokte, pa gljivice. Ako je svaki mogući način skidanja jednako vjerojatan, odredite vjerojatnost da Simeon skine sve sa ruku prije nego što je skinuo sve s barem jedne noge. [/lang] [lang=en] Simeon has on his hands gloves, rings, and nail polish. On his feet, he has official MNM sneakers, Photomath socks, nail polish, fungus, and all of that is wrapped in plastic bags which he stole at MNM’s expense. Simeon must also perform his administrative MNM duties and prepare for exams, so he randomly chooses what to take off next. Simeon can only remove items from his hands and feet in a logical order. He cannot remove the nail polish or rings from his hands until he has taken off the gloves, but after removing the gloves, he may freely remove either the nail polish or the rings. For his feet, he must first remove the plastic bag, then the sneaker, then the sock, then the nail polish, and finally the fungus. If every possible sequence of removing items is equally likely, determine the probability that Simeon removes everything from his hands before he has removed everything from at least one of his feet. [/lang]