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Консультация № 138151
27.05.2008, 18:19
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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
27.05.2008, 23:32
общий
это ответ
Здравствуйте, Sashka!
Всего 5 цифр, в каждое из чисел входят 2, 3 и 5.
Кроме этих цифр входят ещё две из следующих шести: 1, 4, 6, 7, 8, 9.
Эти две цифры можно выбрать C^2_6 (число сочетаний из 6 по 2) способами.
С^2_6 = 6*5/2 = 15.
Таким образом, у нас есть 15 наборов из 5 цифр. В каждом таком наборе
все цифры различны и могут располагаться всеми возможными способами,
количество которых равно 5! = 120.
Таким образом, полное количество чисел, составленных из цифр
от 1 до 9, в каждое из которых входят три заданные цифры,
равно 15*120 = 1800.
Примечание.
Предыдущий ответ соответствует количеству чисел, в которые
входит хотя бы одна из трёх заданных цифр (2,3,5).
Всего 5 цифр, в каждое из чисел входят 2, 3 и 5.
Кроме этих цифр входят ещё две из следующих шести: 1, 4, 6, 7, 8, 9.
Эти две цифры можно выбрать C^2_6 (число сочетаний из 6 по 2) способами.
С^2_6 = 6*5/2 = 15.
Таким образом, у нас есть 15 наборов из 5 цифр. В каждом таком наборе
все цифры различны и могут располагаться всеми возможными способами,
количество которых равно 5! = 120.
Таким образом, полное количество чисел, составленных из цифр
от 1 до 9, в каждое из которых входят три заданные цифры,
равно 15*120 = 1800.
Примечание.
Предыдущий ответ соответствует количеству чисел, в которые
входит хотя бы одна из трёх заданных цифр (2,3,5).
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