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Консультация № 178651
26.05.2010, 01:31
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Уважаемые эксперты, помогите решить задачу.
В купе железнодорожного вагона - 2 дивана по 4 места. Какова вероятность того, что при случайном распределении мест среди 8-ми пассажиров окажутся: 1) 2 определенных лица сидящими друг против друга? 2) 2 определенных лица сидящими рядом?
В купе железнодорожного вагона - 2 дивана по 4 места. Какова вероятность того, что при случайном распределении мест среди 8-ми пассажиров окажутся: 1) 2 определенных лица сидящими друг против друга? 2) 2 определенных лица сидящими рядом?
Обсуждение
26.05.2010, 07:59
общий
26.05.2010, 11:33
это ответ
Здравствуйте, Артем Артемов.
Всего 8 различных пассажиров по 8-ми местам можно расположить 8! = 40320 способами. Для двух конкретных людей:
Число комбинаций, когда два находятся рядом - на каждом диване 3 варианта, на двух диванах - 6 вариантов, и еще умножить на 2, т.к. их можно поменять местами. Итого 6х2=12;
Число комбинаций, когда два находятся напротив - 4 варианта, также умножить на 2, т.к. можно поменять местами. Итого 4х2=8.
Значит, для Иванова и Сидорова, вероятность того, что они:
1) сидят рядом = 12*6!/40320 = 3/14
2) сидят напротив = 8*6!/40320 = 1/7
К каждому благоприятному исходу соответствуют перестановки оставшихся 6-и пассажиров. Это 6!=720
Всего 8 различных пассажиров по 8-ми местам можно расположить 8! = 40320 способами. Для двух конкретных людей:
Число комбинаций, когда два находятся рядом - на каждом диване 3 варианта, на двух диванах - 6 вариантов, и еще умножить на 2, т.к. их можно поменять местами. Итого 6х2=12;
Число комбинаций, когда два находятся напротив - 4 варианта, также умножить на 2, т.к. можно поменять местами. Итого 4х2=8.
Значит, для Иванова и Сидорова, вероятность того, что они:
1) сидят рядом = 12*6!/40320 = 3/14
2) сидят напротив = 8*6!/40320 = 1/7
К каждому благоприятному исходу соответствуют перестановки оставшихся 6-и пассажиров. Это 6!=720
26.05.2010, 09:16
общий
Ulitka71:
Либо уж помножте полученные значения на число перестановок остальных 6-ти человек (6!=720), либо делите число благоприятных расположений не на 8!, а на 7*8=56.
Либо уж помножте полученные значения на число перестановок остальных 6-ти человек (6!=720), либо делите число благоприятных расположений не на 8!, а на 7*8=56.
26.05.2010, 11:26
общий
Да, нужно исправление ошибки. К каждому благоприятному исходу соответствуют перестановки оставшихся 6-и пассажиров. Это 6!=720. Т.е.
1) 12*6!/40320 = 3/14
2) 8*6!/40320 = 1/7
1) 12*6!/40320 = 3/14
2) 8*6!/40320 = 1/7
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