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Консультация № 197234
27.11.2019, 10:16
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Здравствуйте! Прошу помощи в следующем вопросе:
Задача по комбинаторике. Из бригады, в которой работают 10 человек, 5 должны уехать в командировку. Сколько может быть различных составов этой группы, если бригадир и его заместитель одновременно уезжать не должны?
Задача по комбинаторике. Из бригады, в которой работают 10 человек, 5 должны уехать в командировку. Сколько может быть различных составов этой группы, если бригадир и его заместитель одновременно уезжать не должны?
Обсуждение
08.08.2022, 06:26
общий
это ответ
Здравствуйте, sasha181999_9!
Возможны три вида различных составов группы из пяти человек, которая может уехать в командировку:
1) без бригадира и его заместителя. Такая группа может быть набрана
способами;
2) без бригадира, но с его заместителем. Такая группа может быть набрана
способами;
3) без заместителя бригадира, но с бригадиром. Такая группа может быть набрана способами.
Следовательно, может быть
составов группы для поездки в командировку.
Задачу можно решить иначе, если из количества всех возможных составов по пять человек отнять количество составов, в котором есть и бригадир и его заместитель:
Получили такой же ответ.
Возможны три вида различных составов группы из пяти человек, которая может уехать в командировку:
1) без бригадира и его заместителя. Такая группа может быть набрана
способами;2) без бригадира, но с его заместителем. Такая группа может быть набрана
способами;3) без заместителя бригадира, но с бригадиром. Такая группа может быть набрана
способами.Следовательно, может быть
составов группы для поездки в командировку.Задачу можно решить иначе, если из количества всех возможных составов по пять человек отнять количество составов, в котором есть и бригадир и его заместитель:
Получили такой же ответ.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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