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Консультация № 197192
24.11.2019, 16:22
0.00 руб.
26.11.2019, 10:45
0
4
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Колода содержит 52 карты. 1). Сколькими способами можно выбрать 4 карты разных мастей? 2). Сколькими способами можно выбрать 4 карты разных мастей так, чтобы не было ни одной пары одинаковых (т.е. двух королей, двух девяток и т.д.)?
Колода содержит 52 карты. 1). Сколькими способами можно выбрать 4 карты разных мастей? 2). Сколькими способами можно выбрать 4 карты разных мастей так, чтобы не было ни одной пары одинаковых (т.е. двух королей, двух девяток и т.д.)?
Обсуждение
26.11.2019, 10:46
общий
Обратите внимание на эту консультацию, перенесенная из другой рассылки
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
29.11.2019, 16:31
общий
это ответ
Здравствуйте, sasha181999_9!
1) Всего у нас 52 карты (по 13 каждой масти). Первая карта может быть любой из 52. Вторая - любой из не принадлежащих к той же масти, что и первая, то есть - из 39 (52-13). Третья - любая карта двух оставшихся мастей, то есть из 26 карт. И четвёртая - одна из 13 карт оставшейся масти. То есть всего 52[$183$]39[$183$]26[$183$]13 = 685464 вариантов.
2) Аналогично первому варианту, первая карта может быть любой из 52. Вторая должна не совпадать с первой по масти (52-13=39) и по номиналу (минус ещё 3 карты других мастей и того же достоинства), то есть остаётся 36 вариантов. Третья не совпадает с первыми двумя по масти (26 вариантов) и по номиналу (минус ещё по 2 карты каждой из двух оставшихся мастей) - 22 варианта. Четвёртая карта выбирается оставшейся масти (13 вариантов), но не совпадающая с первыми тремя, то есть - из 10. Итого получается 52[$183$]36[$183$]22[$183$]10 = 411840 вариантов.
1) Всего у нас 52 карты (по 13 каждой масти). Первая карта может быть любой из 52. Вторая - любой из не принадлежащих к той же масти, что и первая, то есть - из 39 (52-13). Третья - любая карта двух оставшихся мастей, то есть из 26 карт. И четвёртая - одна из 13 карт оставшейся масти. То есть всего 52[$183$]39[$183$]26[$183$]13 = 685464 вариантов.
2) Аналогично первому варианту, первая карта может быть любой из 52. Вторая должна не совпадать с первой по масти (52-13=39) и по номиналу (минус ещё 3 карты других мастей и того же достоинства), то есть остаётся 36 вариантов. Третья не совпадает с первыми двумя по масти (26 вариантов) и по номиналу (минус ещё по 2 карты каждой из двух оставшихся мастей) - 22 варианта. Четвёртая карта выбирается оставшейся масти (13 вариантов), но не совпадающая с первыми тремя, то есть - из 10. Итого получается 52[$183$]36[$183$]22[$183$]10 = 411840 вариантов.
4
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