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Консультация № 188655
16.01.2016, 22:51
0.00 руб.
17.01.2016, 08:13
0
2
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Перестановка чисел от 1 до N – это последовательность из чисел от 1 до N, записанных в произвольном порядке, такая, что каждое число встречается в ней ровно один раз.
Сколько существует перестановок чисел от 1 до 7 таких, что на позициях 3, 4 и 5 стоят четные числа?
Перестановка чисел от 1 до N – это последовательность из чисел от 1 до N, записанных в произвольном порядке, такая, что каждое число встречается в ней ровно один раз.
Сколько существует перестановок чисел от 1 до 7 таких, что на позициях 3, 4 и 5 стоят четные числа?
Обсуждение
17.01.2016, 08:15
общий
Обратите, пожалуйста, внимание на эту консультацию.
Об авторе:
Facta loquuntur.
Facta loquuntur.
17.01.2016, 08:32
общий
это ответ
Здравствуйте, Посетитель - 399097!
Натуральный ряд чисел от 1 до 7 содержит три чётных числа: 2, 4, 6. Остальные четыре числа - нечётные. Разместить три чётных числа по трём местам можно A[sub]3[/sub][sup]3[/sup] способами. Каждому такому размещению чётных чисел соответствует A[sub]4[/sub][sup]4[/sup] способов размещения четырёх нечётных чисел по четырём местам. Значит, всего существует n=A[sub]3[/sub][sup]3[/sup]*A[sub]4[/sub][sup]4[/sup]=(3!/(3-3)!)*(4!/(4-4)!)=3!*4!=6*24=144 перестановки чисел от 1 до 7 таких, что на позициях 3, 4, 5 стоят чётные числа.
С уважением.
Натуральный ряд чисел от 1 до 7 содержит три чётных числа: 2, 4, 6. Остальные четыре числа - нечётные. Разместить три чётных числа по трём местам можно A[sub]3[/sub][sup]3[/sup] способами. Каждому такому размещению чётных чисел соответствует A[sub]4[/sub][sup]4[/sup] способов размещения четырёх нечётных чисел по четырём местам. Значит, всего существует n=A[sub]3[/sub][sup]3[/sup]*A[sub]4[/sub][sup]4[/sup]=(3!/(3-3)!)*(4!/(4-4)!)=3!*4!=6*24=144 перестановки чисел от 1 до 7 таких, что на позициях 3, 4, 5 стоят чётные числа.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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