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Сколькими способами можно разделить 14 спортсменов на две команды по 7?
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Предмет:
Математика -
Автор:
shelly - 6 лет назад
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Ответы 2
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Умница!
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Автор:
monabarry - 6 лет назад
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0
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Нам из 14 спортсменов нужно выбрать 7 для первой команды, причем порядок выбора не имеет значения. Таким образом, нужно найти число сочетаний из 14 элементов по 7.
С⁷₁₄=14!/(7!(14-7)!)=14!/(7!*7!)=(8*9*10*11*12*13*14*)/(1*2*3*4*5*6*7)=3432
Т.к. нам всё равно, какая команда первая, какая вторая, а каждая пара команд учитывается дважды, то эти способы нужно разделить пополам.
3432÷2=1716 способами можно разделить 14 спортсменов на две команды по 7 человек.
Ответ: 1716 способов.
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Автор:
phantomtr9o - 6 лет назад
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