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Консультация № 176575
08.02.2010, 20:46
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Здравствуйте, эксперты.
Прошу проверить задачу:
Сколькими различными способами можно рассадить 12 человек за 2 стола по 6 мест за каждом. Придумать, как можно различать раcсадки и решить для каждого варианта.
У меня получилось: За 1 стол - сочетание из 12 по 6: C (12, 6) = 924.
За 2 стол: Количество перестановок оставшихся 6: 6!
В итоге вариантов: 924 * 6!
А какие еще могут быть рассадки? Предложите ваш вариант.
Прошу проверить задачу:
Сколькими различными способами можно рассадить 12 человек за 2 стола по 6 мест за каждом. Придумать, как можно различать раcсадки и решить для каждого варианта.
У меня получилось: За 1 стол - сочетание из 12 по 6: C (12, 6) = 924.
За 2 стол: Количество перестановок оставшихся 6: 6!
В итоге вариантов: 924 * 6!
А какие еще могут быть рассадки? Предложите ваш вариант.
Обсуждение
Неизвестный
08.02.2010, 21:36
общий
это ответ
Здравствуйте, Иванов Андрей Владимирович.
На мой взгляд, общее количество вариантов- это размещение 12 человек за 12 мест
P(12)=12! = 479001600
На мой взгляд, общее количество вариантов- это размещение 12 человек за 12 мест
P(12)=12! = 479001600
Неизвестный
08.02.2010, 21:45
общий
это ответ
Здравствуйте, Иванов Андрей Владимирович.
Ваше решение не совсем корректно.
Если все места различимы (например, пронумерованы), то разместить 12 за 2 стола по 6 мест всё равно что разместить 12 человек по 12 местам, т.е. число вариантов 12! = 479001600.
Если же различать только номер стола, тогда задача сводится к вопросу как разбить 12 человек на 2 группы по 6 человек. В этом случае число вариантов С(12, 6) = 924.
Ваше решение не совсем корректно.
Если все места различимы (например, пронумерованы), то разместить 12 за 2 стола по 6 мест всё равно что разместить 12 человек по 12 местам, т.е. число вариантов 12! = 479001600.
Если же различать только номер стола, тогда задача сводится к вопросу как разбить 12 человек на 2 группы по 6 человек. В этом случае число вариантов С(12, 6) = 924.
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