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Консультация № 197228
27.11.2019, 10:11
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Задача по комбинаторике. Сколько различных 6-разрядных десятичных кодов можно образовать, не используя нуля, если каждый код должен состоять из 3-х четных и 3-х нечетных цифр, причем никакая цифра не должна повторяться
Задача по комбинаторике. Сколько различных 6-разрядных десятичных кодов можно образовать, не используя нуля, если каждый код должен состоять из 3-х четных и 3-х нечетных цифр, причем никакая цифра не должна повторяться
Обсуждение
09.08.2022, 07:23
общий
это ответ
Здравствуйте, sasha181999_9!
Поскольку цифра 0, согласно условию задачи, при составлении кода не используется, постольку можно использовать четыре чётные цифры (2, 4, 6, 8) и пять нечётных цифр (1, 3, 5, 7, 9).
Выбрать три различные чётные цифры из четырёх можно
способами. Расставить выбранные цифры по трём местам можно 
способами. Поэтому чётные цифры могут участвовать в формировании кода 
способами.
Выбрать три различные нечётные цифры из пяти можно
способами. Расставить выбранные цифры по трём оставшимся местам можно 
способами. Поэтому нечётные цифры могут участвовать в формировании кода 
способами.
Значит, искомое количество кодов составляет
Поскольку цифра 0, согласно условию задачи, при составлении кода не используется, постольку можно использовать четыре чётные цифры (2, 4, 6, 8) и пять нечётных цифр (1, 3, 5, 7, 9).
Выбрать три различные чётные цифры из четырёх можно
способами. Расставить выбранные цифры по трём местам можно способами. Поэтому чётные цифры могут участвовать в формировании кода способами.Выбрать три различные нечётные цифры из пяти можно
способами. Расставить выбранные цифры по трём оставшимся местам можно способами. Поэтому нечётные цифры могут участвовать в формировании кода способами.Значит, искомое количество кодов составляет
Об авторе:
Facta loquuntur.
Facta loquuntur.
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