Math topic中文

Counting principles

Addition and multiplication principles for counting.

Practice questions

  1. 1A personality test assesses 32 key traits. These 32 traits are grouped into 4 domains - Cognition, Influence, Rapport an…
  2. 2An amateur music composer is arranging a sequence of four musical notes followed by three beats. There are 7 possible no…
  3. 3Kelly 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…
  4. 4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…
  5. 5把10个苹果分成三堆，要求每堆至少1个，至多5个，则不同的分法共有（ ） A. 4种 B. 5种 C. 6种 D. 7种
  6. 6Kitty has 5 small, 3 medium and 2 large spherical charms and each of the 10 charms is uniquely designed. Kitty arranges…
  7. 7How 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?…
  8. 8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？ (…
  9. 9By the end of 2022, the percentages of a population who has received V dose(s) of Covid-19 vaccine are shown in the tabl…
  10. 10The letters from the word PERIMETER are arranged in a row. Find the number of different arrangements of the nine letters…
  11. 11Two married couples, two single adults and two children formed a team of 8 to take part in a series of games. In the fir…
  12. 12设A是整数集的一个非空子集，对于k∈A，如果k-1∉A，且k+1∉A，那么称k是A的一个“好元素”．给定S={1，2，3，4，5，6，7，8}，由S的3个元素构成的所有集合中，不含“好元素”的集合共有（ ） A. 6个 B. 12个 C.…
  13. 13Twelve students from three CCAs organised an overseas learning trip to Shanghai. It comprises five students from Tennis,…
  14. 14用1，0，3，5，6组成四位数，一共可组成 个．
  15. 15从3名男生和2名女生中，安排一名男生和一名女生去打扫卫生，则有 ▲ 种安排方式。
  16. 16Find how many positive integers, less than 1000, are odd numbers. odd numbers which are not divisible by 5. Find the sum…
  17. 17Section B: Probability and Statistics [60 marks] The basketball club in a college has 5 centers, 8 forwards and 7 guards…
  18. 18In a particular year, a company awards scholarships to 4 applicants from a group of nn applicants. If the order of sele…
  19. 19The basketball club in a college has 5 centers, 8 forwards and 7 guards. With the National School Games approaching, the…
  20. 20某单位决定从44名男党员干部和33名女党员干部中选取33人赴外地考察学习，若选出的33人中既有男党员干部又有女党员干部，则不同的选取方案共有()(\quad) A. 6060种 B. 3434种 C. 3131…
  21. 21Two families plan to go on a hiking trip together. There are 10 people from the Lee family, consisting of 3 married coup…
  22. 22用数字00，11，22，33，44组成没有重复数字的五位数，其中偶数的个数为()(\quad) A. 5454 B. 6060 C. 7272 D. 120120
  23. 23Two fair n-sided dice, each with faces numbered 1, 2, ..., n, (where n≥4n \ge 4) are tossed in an experiment. The n…
  24. 24An office team of 10 people includes 7 men and 3 women named Anne, Beth, and Cathie. For an upcoming fire drill exercise…
  25. 25将四棱锥S−ABCDS-ABCD的每一个顶点染上一种颜色，并使同一条棱上的两端异色，如果有恰有55种颜色可供使用，则不同的染色方法有()(\quad) A. 480480种 B. 360360种 C. 420420种 D. 320320…
  26. 26从集合{0,1,2,3,4,5}\{0,1,2,3,4,5\}中任取两个互不相等的数aa，bb组成复数a+bia+bi，其中虚数有( )个． A. 3636 B. 3030 C. 2525 D. 2020
  27. 27下列五个数中，偶数共有 ___ 个，质数共有 ___ 个；从这五个数中选两个相加，和是奇数的选法共有 ___ 种。 11，22，4646，9191，111111。
  28. 28In a strategy game called Colour Clash, players draw coloured orbs from a magical pouch to determine their elemental p…
  29. 29A committee consisting of six people is to be selected from five women and six men. Three of the women are sisters. Find…
  30. 30Three friends, Andy, Ben and Charlie, attend a graduation lunch with their parents. How many ways can the nine people be…
  31. 31高一某次演讲比赛，原有5名同学参加，后又增加2名同学参赛，如果原来5名同学比赛顺序不变，那么不同的比赛顺序有（ ） A. 42种 B. 36种 C. 30种 D. 12种
  32. 32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.
  33. 33A card game called "Happy Family" is played with 28 cards, consisting of 7 sets of 4 cards. Each set consists of a fathe…
  34. 34A student needs to create a 7-character alpha-numeric passcode (that is, at least one letter and one digit must be inclu…
  35. 35A group of ten people consists of four single women, two single men and 2 couples. The ten people are arranged randomly…
  36. 36A gathering of 12 people break into 3 groups of 4 to play 3 different games: carrom, UNO and bridge. Find the number of…
  37. 37A group of seven people consisting of two single men, three single women and one married couple are arranged to be seate…
  38. 38有55盆互不相同的菊花，其中22盆为白色，22盆为黄色，11盆为红色，现要摆成一排，要求红色菊花在中间，白菊花不相邻，黄色菊花也不相邻，则共有 ___ 种不同的摆放发方法((用数字作答))．
  39. 39爸爸、妈妈和晶晶每人从苹果、梨、香蕉三种水果中挑选了一种不同的水果，他们有几种不同的挑法？
  40. 40The Ang family, the Bao family and the Chew family have three, five and four members respectively. The three families ar…
  41. 41某市汽车牌照号码可以上网自编，但规定从左到右第二个号码只能从字母B、C、D中选择，其他四个号码可以从0至9这十个数字中选择（数字可以重复），某车主第一个号码（从左到右）只想在数字3、5、6、8、9中选择，其他号码只想在1、3、6、9中选择，…
  42. 42Nine gifts, three of which are identical and the rest are distinct, are distributed among five people without restrictio…
  43. 43A 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\}…
  44. 44Find the number of ways in which 4-letter code-words can be obtained from the word ENDANGERED if there are no repeated l…
  45. 45已知集合A={x∣x2+3x−4<0}A=\{x|x^{2}+3x-4 < 0\}，B={x∣x+2x−4<0}.(1)B=\{x| \dfrac {x+2}{x-4} < 0\}.(1)在区间(−4,5)(-4,5)上任取一个实数xx，求“x∈A∩Bx∈A∩B”的概率； (2)设(a,b)(a,b)…
  46. 46

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

  47. 47Some MRT trains have cars featuring 12 seats each. Passengers take the trains to travel from station to station each day…
  48. 48Two digits XX and YY are chosen independently at random from the set of 10 digits {0, 1, 2, . . . , 9}. Events AA and…
  49. 49How 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?…
  50. 5020222022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))
  51. 51小于1000而不能被5和7整除的自然数共有 个．
  52. 52An interest group of 8 members consists of one married couple together with 4 other men and 2 other women. Find the numb…
  53. 5320212021年秋季，教育部明确要求在全国中小学全面推行课后延时服务，实行“5+25+2”服务模式．某校开设了篮球、围棋和剪纸三门课后延时服务课程，某班的44个同学每人选择了其中的一门课程，若每门课程都有人选，则不同的选课方案种数…
  54. 54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
  55. 55娇娇有三顶不同的帽子和三条不同的围巾,一顶帽子搭配一条围巾,共有 （ ___ ） 种不同的搭配方法。
  56. 56Section B: Probability and Statistics [60 marks] Eleven cards each bears a single letter and together they can be ma…
  57. 57The bag contains 6 red discs, 6 green discs, 6 yellow discs and 6 blue discs. The discs are indistinguishable aside from…
  58. 58某班55名学生负责校内33个不同地段的卫生工作，每个地段至少有11名学生的分配方案共有()(\quad) A. 6060种 B. 9090种 C. 150150种 D. 240240种
  59. 59An ice-cream café sells a mega sundae in which the customer will order 5 scoops of ice-cream. The staff will arrange the…
  60. 60Find the number of ways in which the letters of the word PERCEPTIVE can be arranged if all the vowels are separated; the…