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Консультация № 138146
27.05.2008, 18:14
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Здравствуйте уважаемые эксперты!
Помогите пожалуйста с такой задачкой:
Сколько можно сформировать разных 5-значных чисел (в десятичной системе), в которых все цифры разные, и чтобы были цифры 2, 3 и 5, но не должно быть цифры 0.
Если можно с обьяснениями. Заранее спасибо!!!
Помогите пожалуйста с такой задачкой:
Сколько можно сформировать разных 5-значных чисел (в десятичной системе), в которых все цифры разные, и чтобы были цифры 2, 3 и 5, но не должно быть цифры 0.
Если можно с обьяснениями. Заранее спасибо!!!
Обсуждение
Неизвестный
27.05.2008, 20:06
общий
это ответ
Здравствуйте, Sashka!
Будем рассуждать логически
Вообще каждой из 5 цифр пятизначного числа может стоять 10 цифр, но мы исключаем 0, и тогда их остается 9.
Далее цифры не должны повторяться, значить на 1ом месте может стоять одна из 9, потом одна из 8 оставшихся и т.д. будет 9*8*7*6*5 также должна быть одна из цифр равная 2 3 или 5, легче посчитать комбинации без этих цифр, а потом вычесть кол-во комбинаций из общего числа
у нас на 1ом место может стоять одна из уже только 6 цифр, на 2ом одна из 5 оставшихся и т.д. получается 6*5*4*3*2
а теперь вычтем из общего числа кол-во тех комбинаций в которых нет ни 2, ни 3, ни 5
9*8*7*6*5 - 6*5*4*3*2=14400
Удачи
Интересная задача
Будем рассуждать логически
Вообще каждой из 5 цифр пятизначного числа может стоять 10 цифр, но мы исключаем 0, и тогда их остается 9.
Далее цифры не должны повторяться, значить на 1ом месте может стоять одна из 9, потом одна из 8 оставшихся и т.д. будет 9*8*7*6*5 также должна быть одна из цифр равная 2 3 или 5, легче посчитать комбинации без этих цифр, а потом вычесть кол-во комбинаций из общего числа
у нас на 1ом место может стоять одна из уже только 6 цифр, на 2ом одна из 5 оставшихся и т.д. получается 6*5*4*3*2
а теперь вычтем из общего числа кол-во тех комбинаций в которых нет ни 2, ни 3, ни 5
9*8*7*6*5 - 6*5*4*3*2=14400
Удачи
Интересная задача
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