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Консультация № 193057
09.04.2018, 09:30
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Здравствуйте, уважаемые эксперты! Пожалуйста, ответьте на вопрос:
N человек, в том числе A и B , располагаются в ряд. Сколькими способами можно разместить A и B так, чтобы между ними было ровно r человек?
N человек, в том числе A и B , располагаются в ряд. Сколькими способами можно разместить A и B так, чтобы между ними было ровно r человек?
Обсуждение
09.04.2018, 12:01
общий
Адресаты:
У Вас есть какие-нибудь собственные соображения по решению этой задачи?
Об авторе:
Facta loquuntur.
Facta loquuntur.
09.04.2018, 12:04
общий
09.04.2018, 12:05
Адресаты:
Возможно нужно каким-то образом правильно использовать формулу сочетания.
09.04.2018, 12:32
общий
Адресаты:
Я предлагаю Вам не спешить и порассуждать. Сначала нужно вычислить, сколько существует способов выделить два места для A и B при известных N и r.
Предположим N=10, какие значения может принимать r?
Предположим N=10, какие значения может принимать r?
Об авторе:
Facta loquuntur.
Facta loquuntur.
11.04.2018, 10:19
общий
это ответ
Здравствуйте, yarikbmw13@yandex.ru!
К сожалению, Вы не захотели продолжить обсуждение задачи в мини-форуме консультации. Поэтому я изложу только свои соображения по решению.
Пусть имеется N мест, расположенных в ряд, и N человек. Усадим на первое место человека A, а через r мест, то есть на N-(r+2)-е место -- человека B. На оставшихся N-(r+2) местах остальных людей можно рассадить (N-(r+2))! способами.
Тот же результат будет, если A и B поменяются местами.
Существует N-(r+2) способов усадить A и B так, чтобы между ними было ровно r мест (не человек!).
Остаётся сделать вывод.
Разумеется, я мог ошибиться в своих рассуждениях.
К сожалению, Вы не захотели продолжить обсуждение задачи в мини-форуме консультации. Поэтому я изложу только свои соображения по решению.
Пусть имеется N мест, расположенных в ряд, и N человек. Усадим на первое место человека A, а через r мест, то есть на N-(r+2)-е место -- человека B. На оставшихся N-(r+2) местах остальных людей можно рассадить (N-(r+2))! способами.
Тот же результат будет, если A и B поменяются местами.
Существует N-(r+2) способов усадить A и B так, чтобы между ними было ровно r мест (не человек!).
Остаётся сделать вывод.
Разумеется, я мог ошибиться в своих рассуждениях.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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