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수학동아 - 폴리매스
함께 풀고 싶은 문제
나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.
우럭
2022.05.15 00:16
조회 155
당신에게 1부터 연속된 8개의 수를 임의로 배열한 수열이 주어진다.
다만, 당신은 이 수열이 어떻게 배열되어 있는지 알 수 없다.
당신은 수열의 첫 항부터 마지막 항까지 이동하며, 순서대로 그 항의 수를 알게 된다.
이때, 다음 물음에 답해보자.
1) 4째 항 이하에서 3보다 작은 수가 적어도 하나 포함될 확률을 기약분수로 나타내시오.
좋다. 그러면 당신이 조합의 기본은 할 수 있다고 생각하고, 넘어가도록 하자.
앞에서, 우리는 한 항별로 이동하며 그 항의 수를 알아낸다고 했다.
즉, 우리는 아직 확인하지 못한 항에 적힌 수를 알지 못한다.
이 사실을 알고, 다음 질문을 답해보자.
2) 당신은 현재 2번째 항에 적힌 수까지 확인했으며, 차례대로 6과 2였다고 한다.
이때, 이 수열에서 길이 3 이상의 최대 공통 부분 서열 (LIS)가 나타나지 않을 확률을 분수로 구하시오.
각 문항당 해결 1개이며, 풀이를 써주기 바란다.
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Amath
Lv.8
2022.05.15 21:23
이 수열은 1에서 8까지의 정수로 이루어진 수열인가요?
-
우럭
Lv.9
2022.05.16 04:51
좋아요0
-
Amath
Lv.8
2022.05.16 16:42
4째 항 이하는 1-4째 항을 말하는 건가요, 4-8째 항을 말하는 건가요?
지금 바로
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