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수학동아 - 폴리매스
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
[창의 퍼즐] 롤로 수학문제 만든느 시리즈 4. 픽 + 밴
켋
2020.04.08 08:57
조회 489
지난번 문제에서는 픽만을 생각했다.
그런데, 랭크 게임에서는 밴도 따진다.
즉, 각각의 플레이어는 한 챔피언 사용을 금지시킨다. 이때, 상대팀과 우리팀이 같은 챔피언을 밴 할수는 있으나, 같은 팀에서 여러 명이 한 챔피언을 밴할 수는 없다.
즉, 내가 가렌을 하고 싶은데 상대팀이 밴을 한 다섯 명의 챔피언 중 가렌이 포함되어 있으면, 가렌을 플레이할 수 없다.
하나의 '전제된 특수한 게임'을 플레이하고 있는 10명의 플레이어에 대하여,
각각의 플레이어는 148명의 챔피언 중 한가지의 챔피언을 배정받는다(조합따위는 신경쓰지 않고, 중복된 챔피언을 배정받지 않는다. 즉, 두명 이상이 가렌을 배정받지 못한다)
각각의 플레이어는 아군, 즉 자신을 제외한 네 명이 어떤 챔피언을 배정받았는지는 알고 있으나, 상대 5명이 배정받은 챔피언은 모른다.
이 상태에서, 각각의 플레이어는 아군이 배정받은 5명의 챔피언을 제외한, 나머지 143명의 챔피언 중 하나를 랜덤으로 밴한다고 했을 때, 밴을 마친 후 모든 플레이어가 배정받은 챔피언을 플레이 할 수 있을 확률은 얼마인가?
지금 바로
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