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Консультация № 197225
27.11.2019, 10:09
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Задача по комбинаторике. В турнире участвуют 10 команд. 1) Сколькими способами можно составить расписание игр одного тура? 2) В скольких вариантах 2 самые сильные команды будут играть между собой?
Задача по комбинаторике. В турнире участвуют 10 команд. 1) Сколькими способами можно составить расписание игр одного тура? 2) В скольких вариантах 2 самые сильные команды будут играть между собой?
Обсуждение
10.08.2022, 07:44
общий
это ответ
Здравствуйте, sasha181999_9!
По-моему, предложенная задача сформулирована неоднозначно: неизвестно, имеет ли значение порядок команд в паре и сколько туров в турнире уже сыграно. Поэтому будем исходить из предположений, что порядок команд в паре не имеет значения и требуется составить расписание первого тура. Тогда получим следующие результаты.
1) Две команды из десяти для первой пары можно выбрать
способами; две команды из оставшихся восьми для второй пары можно выбрать 
способами; две команды из оставшихся шести для третьей пары можно выбрать 
способами; две команды из оставшихся четырёх для четвёртой пары можно выбрать 
способами; две команды из оставшихся двух для пятой пары можно выбрать одним способом. Значит, искомое количество способов равно 
2) Если две самые сильные команды играют между собой, то первая пара уже выбрана одним способом. Для остальных пар остаются в силе указанные выше количества способов их составления. Поэтому искомое количество способов равно
По-моему, предложенная задача сформулирована неоднозначно: неизвестно, имеет ли значение порядок команд в паре и сколько туров в турнире уже сыграно. Поэтому будем исходить из предположений, что порядок команд в паре не имеет значения и требуется составить расписание первого тура. Тогда получим следующие результаты.
1) Две команды из десяти для первой пары можно выбрать
способами; две команды из оставшихся восьми для второй пары можно выбрать способами; две команды из оставшихся шести для третьей пары можно выбрать способами; две команды из оставшихся четырёх для четвёртой пары можно выбрать способами; две команды из оставшихся двух для пятой пары можно выбрать одним способом. Значит, искомое количество способов равно 2) Если две самые сильные команды играют между собой, то первая пара уже выбрана одним способом. Для остальных пар остаются в силе указанные выше количества способов их составления. Поэтому искомое количество способов равно
Об авторе:
Facta loquuntur.
Facta loquuntur.
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