[理工] [離散]-排列組合

看板Grad-ProbAsk作者Austin9 (奧斯丁)時間14年前 (2010/07/01 00:11)推噓1(1推 0噓 17→)

留言18則, 2人參與討論串17/19 (看更多)

1.In a row of 20 seats,in how many ways can three blocks of consecutive seats with five seats in each block be selected? ans: 8!/5!3! 不懂為什麼是這個答案說？ 2.Cards are drawn from a dck of 52 cards with replacement.In how many ways can 10 cards be drawn so that the 10th cards is the first repeatition (b) repeat part (a) if the 10th card is a repeatition. (b)ans 52^10-52*51^9 這答案怎麼來的啊？不懂說 3.In how many ways can two adjacent squares be selected from an 8*8 chessboard? ans 8(8-1)+8(8-1) 這也是不懂 4.In how many ways can 22 different books be given to 5 student so that 2 of them will have books and the order 3 will have 4 books? 我的答案是C(22,5)*C(17,5)*C(12,4)*C(8,4)*C(4,4)但答案多了C(5,2)不知道為什麼要多乘這個？ 5.If we write all decimal number from 1 to 1 million,how many times would we have written the digit 9? 我的答案是..因為從000000~999999所以是10^6，但答案是10^5，想知道那兒錯了？謝謝 6.Determine the number of ways to seat 5 boys in a row of 11 chairs such that no two boys are next to each other 我的想法是5個人先固定所以5!，然後再把6張椅子放到這6個位置就1種方法，但答案是 C(7,2)5!咧？？？為什麼？ 7.Suppose n different games are to distributed among n children.In how many ways can this be done so that exactly one child gets no game? 不懂答案為什麼是C(n,2)*P(n,n-1) 8.A delegation of four students is to be selected from a total of 12 students to attend a meeting (a)in how many ways can the delegation be choosen? (B)repeat part (a) if there are two students who refuse to be in the delegation together? (c)repeat part(a) if there are two students who wil only attend the meeting together? (d)repeat part(a) if there are two students who refuse to be in the delegation together and two students who refuse to be in the delegation together? 我的想法b題答案是C(10,3)但ans是c(2,1)c(10,3) 不懂c的答案是C(10,2)+C(10,4) 不懂d的答案是C(2,1)C(8,1)+C(2,1)C(8,3)(註:第d題的題目覺得應該是抄錯了，但我手邊拿到的就是這樣) 請各位高手解惑一下，謝謝。 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 27.105.35.9

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