高中機率題目(英文)

2011-03-11 3:28 pm

1) a club consisting of 20 members, how many ways are there of choosing a committee of 6 if the club president must be on the committee and another member of the club is not able to serve? ans: 8568

2) At a chess tourment with 12 players, each player played exactly 1 game with all but one of the other players. how many games were played at the tourment?ans:60

3) how many ways can 6 students be seated in a row if 2 particular students must be seated next to each other? ans:240

4) how many positive even integers less than 1000 can be formed from the digits 0,1,2,3,4,5?ans:107

5) how many ways can 6 students be seated in a row if 2 particular ctudents are to be separated? ans: 480

6) I invite 4 couples to dinner and seat them at a round table. how many ways can i arrange them if emn and women sit alternately? ans: 144

7) how many different ways can you answer a 7 question multiple 3 choice exam if you know no two consecutive answers are the same? ans:192

Thanks!

更新1:

will you please explain why?? thank you!

回答 (3)

myisland8132

2011-03-11 8:15 pm

✔ 最佳答案

Solution Outline

(1) 18C5 = 8568

(2) 12*10/2 = 60(3) (5P5)(2!) = 240

(4) 1-digit : 2; 2-digit: 5 + 5 + 5 = 15, 3-digit:5*6 + 5*6 + 5*6 = 90
Total:107

(5) (4!)(5P2) = 24*20 = 480(6) First, for each man, assigns the woman to him (4!). Then arrange these 4 pairs to the round table (3!). no. of ways = 144

(7) 3(2^6) = 192

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月下隱者

2011-03-11 9:45 pm

6)
3!*4!
先排男，再塞進去女的

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旺旺

2011-03-11 5:26 pm

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