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Консультация № 197224
27.11.2019, 10:08
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Задача по комбинаторике. В купе железнодорожного вагона - два дивана по 3 места. Сколькими способами могут разместиться в нем 6 пассажиров, если 2 человека хотят сидеть лицом к локомотиву, 1 - спиной, остальным трем это безразлично?
Задача по комбинаторике. В купе железнодорожного вагона - два дивана по 3 места. Сколькими способами могут разместиться в нем 6 пассажиров, если 2 человека хотят сидеть лицом к локомотиву, 1 - спиной, остальным трем это безразлично?
Обсуждение
01.12.2019, 09:56
общий
это ответ
Здравствуйте, sasha181999_9!
Число способов разместить двух человек лицом к локомотиву на соответствующем трёхместном диване равно
(здесь используем число перестановок, а не сочетаний, поскольку имеет значение не только, какие места будут заняты, но и в каком порядке). Человека, желающего ехать спиной, можно разместить 3 способами на одном из трёх мест второго дивана, причём независимо от того, как сели первые двое, поэтому для этих трёх человек будет 3[$183$]6 = 18 способов размещения. Для остальных 3 человек число способов разместить их на трёх свободных местах будет всегда равно
следовательно, общее число способов размещения при данных условиях составит 18[$183$]6 = 108.
Число способов разместить двух человек лицом к локомотиву на соответствующем трёхместном диване равно
(здесь используем число перестановок, а не сочетаний, поскольку имеет значение не только, какие места будут заняты, но и в каком порядке). Человека, желающего ехать спиной, можно разместить 3 способами на одном из трёх мест второго дивана, причём независимо от того, как сели первые двое, поэтому для этих трёх человек будет 3[$183$]6 = 18 способов размещения. Для остальных 3 человек число способов разместить их на трёх свободных местах будет всегда равно
следовательно, общее число способов размещения при данных условиях составит 18[$183$]6 = 108.
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