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Консультация № 197238
27.11.2019, 10:18
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Здравствуйте! У меня возникли сложности с таким вопросом:
Задача по комбинаторике. Сколько слов можно получить, переставляя буквы в слове ГОРА? В слове ИНСТИТУТ ?
Задача по комбинаторике. Сколько слов можно получить, переставляя буквы в слове ГОРА? В слове ИНСТИТУТ ?
Обсуждение
06.08.2022, 22:33
общий
это ответ
Здравствуйте, sasha181999_9!
В слове "гора" четыре буквы, причём все они различны. Поэтому искомое количество слов равно количеству перестановок четырёх различных элементов и составляет
В слове "институт" восемь букв, причём буквы "н", "с", "у" встречаются по одному разу, буква "и" встречается два раза, буква "т" встречается три раза. Поэтому выбрать одно место для буквы "н" можно восемью способами, одно место для буквы "с" -- семью способами, одно место для буквы "у" -- шестью способами, два места для буквы "и" --
способами, три места для буквы "т" -- одним способом. Значит, искомое количество слов составляет 
В слове "гора" четыре буквы, причём все они различны. Поэтому искомое количество слов равно количеству перестановок четырёх различных элементов и составляет
В слове "институт" восемь букв, причём буквы "н", "с", "у" встречаются по одному разу, буква "и" встречается два раза, буква "т" встречается три раза. Поэтому выбрать одно место для буквы "н" можно восемью способами, одно место для буквы "с" -- семью способами, одно место для буквы "у" -- шестью способами, два места для буквы "и" --
способами, три места для буквы "т" -- одним способом. Значит, искомое количество слов составляет
Об авторе:
Facta loquuntur.
Facta loquuntur.
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