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Консультация № 187783
10.03.2014, 20:30
94.77 руб.
0
3
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Из колоды в 36 карт вынимают n=7 карт. Указать число наборов, содержащих ровно m=2 карт бубновой масти и k=2 карт пиковой масти. Рассмотреть случаи выбора с возвращением и без возвращения.
Спасибо!
Из колоды в 36 карт вынимают n=7 карт. Указать число наборов, содержащих ровно m=2 карт бубновой масти и k=2 карт пиковой масти. Рассмотреть случаи выбора с возвращением и без возвращения.
Спасибо!
Обсуждение
10.03.2014, 21:59
общий
это ответ
Здравствуйте, Сидорова Елена Борисовна!
Без возвращения
2 карты из 9 карт бубновой масти можно выбрать C(9,2)=36 способами
2 карты из 9 карт пиковой масти можно выбрать C(9,2)=36 способами
Остальные 3 карты из 18 можно выбрать C(18,3)=816 способами
36*36*816=1057536
С возвращением
Добавляются парные карты
2 карты из 9 карт бубновой масти можно выбрать 36+9=45 способами
2 карты из 9 карт пиковой масти можно выбрать 45 способами
Остальные 3 карты из 18 можно выбрать C(18,3)=816+18+18*17= 1140 способами
45*45*1140 =2308500
Без возвращения
2 карты из 9 карт бубновой масти можно выбрать C(9,2)=36 способами
2 карты из 9 карт пиковой масти можно выбрать C(9,2)=36 способами
Остальные 3 карты из 18 можно выбрать C(18,3)=816 способами
36*36*816=1057536
С возвращением
Добавляются парные карты
2 карты из 9 карт бубновой масти можно выбрать 36+9=45 способами
2 карты из 9 карт пиковой масти можно выбрать 45 способами
Остальные 3 карты из 18 можно выбрать C(18,3)=816+18+18*17= 1140 способами
45*45*1140 =2308500
5
спасибо большое!
10.03.2014, 23:20
общий
Адресаты:
поясните пожалуйста вот эту строку
Остальные 3 карты из 18 можно выбрать C(18,3)=816+18+С(18,2)*17/2= 3435 способами
И еще такой момент. Это решение при неупорядоченном выборе? Что будет в случае упорядоченного.
Спасибо!
Остальные 3 карты из 18 можно выбрать C(18,3)=816+18+С(18,2)*17/2= 3435 способами
И еще такой момент. Это решение при неупорядоченном выборе? Что будет в случае упорядоченного.
Спасибо!
10.03.2014, 23:25
общий
10.03.2014, 23:26
Адресаты:
1 случай - все 3 карты разные, это 816
2 случай - 2 карты одинаковые, одна другая. Тогда выбирается пара, а третья совпадает с первой. Пара выбирается 18*17 способами
3 случай - 3 карты одинаковые, выбирается одна из 18.
В упорядоченном случае все числа умножаются на 7!=5040
2 случай - 2 карты одинаковые, одна другая. Тогда выбирается пара, а третья совпадает с первой. Пара выбирается 18*17 способами
3 случай - 3 карты одинаковые, выбирается одна из 18.
В упорядоченном случае все числа умножаются на 7!=5040
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