Math topic中文

Arrangements

Arrangements of objects in a line or in a circle, including cases involving repetition and restriction.

Practice questions

  1. 1Eight students are shortlisted to be prize recipients for a competition. Two students are awarded the first prize and an…
  2. 2A personality test assesses 32 key traits. These 32 traits are grouped into 4 domains - Cognition, Influence, Rapport an…
  3. 3An amateur music composer is arranging a sequence of four musical notes followed by three beats. There are 7 possible no…
  4. 4Two brothers Kai and Leo are duathlon (running and cycling) athletes who train regularly. For each day, the probability…
  5. 5Colour Vision Deficiency is the decreased ability to see differences in colours. Someone with normal colour vision will…
  6. 6A pair of siblings, Abbey and Betty, went to a book fair with six other friends. The eight of them stood in a queue in r…
  7. 7Kelly has a box of spherical beads labelled with the 26 letters from A to Z, all of which have the same size. For each l…
  8. 8In a social club with 1000 members, the executive committee would like to survey the members' opinion on the activities…
  9. 9为弘扬我国古代的“六艺”文化，某夏令营主办单位计划利用暑期开设“礼”“乐”“射”“御”“书”“数”六门体验课程，每周一门，连续开设六周，则 ()(\quad) A. 某学生从中选三门，共有3030种选法 B. 课程“射”“御”排在不…
  10. 10Kitty has 5 small, 3 medium and 2 large spherical charms and each of the 10 charms is uniquely designed. Kitty arranges…
  11. 11How many six-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 if repetition of digits is not allowed?…
  12. 12男运动员44名，女运动员33名，其中男女队长各11人，现77名运动员排成一排。 (1)如果女运动员全排在一起，有多少种排法？ (2)如果女运动员都不相邻，有多少种排法？ (3)如果女运动员不站两端，有多少种排法？ (…
  13. 13The letters from the word PERIMETER are arranged in a row. Find the number of different arrangements of the nine letters…
  14. 14Two married couples, two single adults and two children formed a team of 8 to take part in a series of games. In the fir…
  15. 15Twelve students from three CCAs organised an overseas learning trip to Shanghai. It comprises five students from Tennis,…
  16. 16A team of 15 students was selected for an outdoor education trip. One student volunteered to be the trip leader while an…
  17. 17AA、BB、CC、DD、EE五个人并排站在一起，则下列说法正确的有()(\quad) A. 若AA、BB两人站在一起有2424种方法 B. 若AA、BB不相邻共有7272种方…
  18. 18In a particular year, a company awards scholarships to 4 applicants from a group of nn applicants. If the order of sele…
  19. 19In a supermarket lucky draw, a participant will first spin a wheel, followed by throwing a fair six-sided die. The wheel…
  20. 20An office team of 10 people includes 7 men and 3 women named Anne, Beth, and Cathie. For an upcoming fire drill exercise…
  21. 21The table below shows the number of male and female students studying Chemistry, Physics and Biology at a private school…
  22. 22A committee consisting of six people is to be selected from five women and six men. Three of the women are sisters. Find…
  23. 23A pair of siblings, Abbey and Betty, went to a book fair with six other friends. The eight of them stood in a queue in r…
  24. 24Three friends, Andy, Ben and Charlie, attend a graduation lunch with their parents. How many ways can the nine people be…
  25. 25A bag contains 4 red counters and 6 blue counters. 4 counters are drawn from the bag at random, without replacement. Cal…
  26. 26用数字11，22，33，44，55可以组成没有重复数字，并且比2000020000大的五位偶数共有 ___ 个.
  27. 27A card game called "Happy Family" is played with 28 cards, consisting of 7 sets of 4 cards. Each set consists of a fathe…
  28. 28A student needs to create a 7-character alpha-numeric passcode (that is, at least one letter and one digit must be inclu…
  29. 29A group of ten people consists of four single women, two single men and 2 couples. The ten people are arranged randomly…
  30. 30A group of seven people consisting of two single men, three single women and one married couple are arranged to be seate…
  31. 31A bag contains four red and eight blue balls of which two of the red balls and six of the blue balls have the number "0"…
  32. 32The Ang family, the Bao family and the Chew family have three, five and four members respectively. The three families ar…
  33. 33男数学教师和44位女数学教师选出33位师到33个班任班任班位班主任))，要求这33位班主中女教师都有，则不同的选派方案有()() A. 210210 B. 420420 C. 630630 D. 840840…
  34. 34A code consists of 10 characters. The first 5 characters of the code is formed using 5 letters chosen from the set {A,B,C,D,E,F,G,H}\{A, B, C, D, E, F, G, H\}…
  35. 35Find the number of ways in which 4-letter code-words can be obtained from the word ENDANGERED if there are no repeated l…
  36. 36

    Section B: Statistics [60 marks] A group of 11 people consists of 6 men and 5 women, 3 of whom are sisters. A commit…

  37. 37Some MRT trains have cars featuring 12 seats each. Passengers take the trains to travel from station to station each day…
  38. 38How many six-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 if repetition of digits is not allowed?…
  39. 3920222022年北京冬奥会即将开幕，某校44名学生报名担任志愿者．将这44名志愿者分配到33个比赛场馆，每个比赛场馆至少分配一名志愿者，则所有分配方案共有 ___种．((用数字作答))
  40. 40An interest group of 8 members consists of one married couple together with 4 other men and 2 other women. Find the numb…
  41. 41某市四大高校准备联合举办四校数学竞赛，比赛共4040名额，四校分配，每校不得少于99人，则不同的分配方法有().(). A. 2020种 B. 2828种 C. 3535种 D. 4242种
  42. 42Section B: Probability and Statistics [60 marks] Eleven cards each bears a single letter and together they can be ma…
  43. 4320222022年央视春晚出现了很多优秀的歌曲、小品、相声等节目，现将歌曲《你是我生命中的礼物》《我们的时代》《爱在一起》《春天的钟声》，冬奥主题歌曲《点亮梦》，小品《父与子》《还不还》《喜上加喜》《发红包》《休息区的故事》，相声《欢乐方言…
  44. 44An ice-cream café sells a mega sundae in which the customer will order 5 scoops of ice-cream. The staff will arrange the…
  45. 45Find the number of ways in which the letters of the word PERCEPTIVE can be arranged if all the vowels are separated; the…
  46. 46有A、B、C、D、E、F六张字母卡片，摆成一行，要求A摆在左端，F摆在右端，有 种不同摆法．
  47. 47In this question you should state clearly the values of the parameters of any normal distributions you use. A fruit…
  48. 48Section B: Probability and Statistics [41 marks] A code consists of 10 digits which are either zeros or ones, for exampl…
  49. 49Four boys and three girls are at a playground. In one of their games, all seven of them have to stand in a straight line…
  50. 50A group of 9 friends, including Albert and Ben, are having dinner at Albert's house. They sit in two groups: a row of 4…
  51. 51若55个人站成一排照相，其中甲、乙两人不相邻，则不同的排法种数为___
  52. 52A bag contains 5 cards with the letter 'A', 3 cards with the letter 'B' and 2 cards with the letter 'C'. A A A A A B B B C C\text{A } \text{A } \text{A } \text{A } \text{A } \text{B } \text{B } \text{B } \text{C } \text{C}…
  53. 53有4名同学和2位老师排成一排合影，其中2位老师必须相邻，则不同的排法有 种.（用数字作答）
  54. 54某种产品的加工需要 AA，BB，CC，DD，EE五道工艺，其中 AA必须在DD的前面完成((不一定相邻))，其它工艺的顺序可以改变，但不能同时进行，为了节省加工时间，BB 与CC…