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Консультация № 199580
11.11.2020, 23:14
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом: В соревновании по бегу участвуют 8 человек. На стадионе имеется 5 беговых
дорожек. Во втором забеге оставшиеся три бегуна бегут по первым трем
дорожкам. Сколько вариантов имеется для состава первого забега? Какова
вероятность того, что некий конкретный спортсмен А будет бежать во втором
забеге по первой дорожке?
дорожек. Во втором забеге оставшиеся три бегуна бегут по первым трем
дорожкам. Сколько вариантов имеется для состава первого забега? Какова
вероятность того, что некий конкретный спортсмен А будет бежать во втором
забеге по первой дорожке?
Обсуждение
16.11.2020, 17:18
общий
это ответ
Здравствуйте, Жукнавозник!
Не прибегая к формулам комбинаторики, можно заметить, что при формировании состава первого забега на первую дорожку можно выбрать любого из 8 человек, на вторую - любого из оставшихся семи, на третью, четвёртую и пятую - аналогично одного из оставшихся шести, пяти и четырёх. Таким образом, всего возможно 8[$215$]7[$215$]6[$215$]5[$215$]4 = 6720 вариантов. Поскольку для каждого спортсмена существует восемь возможных позиций (пять дорожек в первом забеге и три во втором), то он может попасть на любую из них (например, на первую дорожку во втором забеге) с одинаковой вероятностью, равной 1/8 = 0.125.
Не прибегая к формулам комбинаторики, можно заметить, что при формировании состава первого забега на первую дорожку можно выбрать любого из 8 человек, на вторую - любого из оставшихся семи, на третью, четвёртую и пятую - аналогично одного из оставшихся шести, пяти и четырёх. Таким образом, всего возможно 8[$215$]7[$215$]6[$215$]5[$215$]4 = 6720 вариантов. Поскольку для каждого спортсмена существует восемь возможных позиций (пять дорожек в первом забеге и три во втором), то он может попасть на любую из них (например, на первую дорожку во втором забеге) с одинаковой вероятностью, равной 1/8 = 0.125.
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