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Консультация № 197222
27.11.2019, 10:07
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Задача по комбинаторике. Из колоды, содержащей 52 карты, вынули 6 карт. В скольких случаях среди этих карт окажется не менее двух тузов?
Задача по комбинаторике. Из колоды, содержащей 52 карты, вынули 6 карт. В скольких случаях среди этих карт окажется не менее двух тузов?
Обсуждение
01.12.2019, 09:20
общий
это ответ
Здравствуйте, sasha181999_9!
В общем случае, если имеется n объектов, разделённых на k групп, содержащих соответственно n[sub]1[/sub], n[sub]2[/sub],...n[sub]k[/sub] объектов (n[sub]1[/sub] + n[sub]2[/sub] + ... + n[sub]k[/sub] = n), и производится выборка m объектов (m[$8804$]n), то число способов выбрать m[sub]1[/sub] объектов из первой группы, m[sub]2[/sub] - из второй,... m[sub]k[/sub] из k-ой группы (m[sub]1[/sub] + m[sub]2[/sub] + ... + m[sub]k[/sub] = m) равно
В данном случае n = 52 (число карт в колоде), k = 2 (тузы и остальные карты), n[sub]1[/sub] = 4 (число тузов в колоде), n[sub]2[/sub] = 48 (число остальных карт), m = 6 (число карт, вынутых из колоды). Далее следует рассмотреть 3 варианта: m[sub]1[/sub] = 2, m[sub]2[/sub] = 4 (вынуто 2 туза), m[sub]1[/sub] = m[sub]2[/sub] = 3 (вынуто 3 туза) и m[sub]1[/sub] = 4, m[sub]2[/sub] = 2 (вынуты все 4 туза). Число способов получить соответствующий вариант равно
Искомое число будет суммой этих значений: 1167480 + 69814 + 1128 = 1237792.
В общем случае, если имеется n объектов, разделённых на k групп, содержащих соответственно n[sub]1[/sub], n[sub]2[/sub],...n[sub]k[/sub] объектов (n[sub]1[/sub] + n[sub]2[/sub] + ... + n[sub]k[/sub] = n), и производится выборка m объектов (m[$8804$]n), то число способов выбрать m[sub]1[/sub] объектов из первой группы, m[sub]2[/sub] - из второй,... m[sub]k[/sub] из k-ой группы (m[sub]1[/sub] + m[sub]2[/sub] + ... + m[sub]k[/sub] = m) равно
В данном случае n = 52 (число карт в колоде), k = 2 (тузы и остальные карты), n[sub]1[/sub] = 4 (число тузов в колоде), n[sub]2[/sub] = 48 (число остальных карт), m = 6 (число карт, вынутых из колоды). Далее следует рассмотреть 3 варианта: m[sub]1[/sub] = 2, m[sub]2[/sub] = 4 (вынуто 2 туза), m[sub]1[/sub] = m[sub]2[/sub] = 3 (вынуто 3 туза) и m[sub]1[/sub] = 4, m[sub]2[/sub] = 2 (вынуты все 4 туза). Число способов получить соответствующий вариант равно
Искомое число будет суммой этих значений: 1167480 + 69814 + 1128 = 1237792.
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