20 городов

*

Категория: 
Сложность: 

В стране 20 городов, каждые два из которых соединены авиалинией. Сколько авиалиний в этой стране?

Решение

Каждая авиалиния соединяет два города. В качестве первого города можно взять любой из 20 городов (город A), а в качестве второго — любой из 19 оставшихся (город B). Перемножив эти числа, получаем 20 × 19 = 380. Однако при этом подсчёте каждая авиалиния учтена дважды (первый раз, когда в качестве первого города был выбран город A, а второго — город B, а второй раз — наоборот). Таким образом, число авиалиний равно 380 : 2 = 190.




Комментарии

преподаватель просит какую то схему по этой задаче. Что за схема и вобще какие бывают схемы комбинаторики?

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