Math topic中文

Permutation combination

Concepts of permutation (nPr^nP_r) and combination (nCr^nC_r).

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. 3Alice has 24 apples. In how many ways can she share them with Becky and Christ so that each of the three people has at l…
  4. 4Abby, Bridget, and four of their classmates will be seated in two rows of three for a group picture, as shown.If the sea…
  5. 5学校进行羽毛球选拔赛，每个参赛选手都要和其他所有选手赛一场．若有20人参赛，那么一共要进行 场选拔赛．
  6. 6Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. H…
  7. 7若C17x=C172x−1C_{17}^{x}=C_{17}^{2x-1}，则正整数xx的值是()(\quad) A. 11 B. 44 C. 66 D. 88
  8. 8Kelly 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…
  9. 9Events AA and BB are such that P(A)=0.7P(A)=0.7 and P(B)=0.8P(B)=0.8. Show that P(A∩B)≥0.5P(A \cap B) \ge 0.5 If P(A′ ∪ B)=0.85P(A'\ \cup\ B)=0.85,…
  10. 10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…
  11. 11Kitty has 5 small, 3 medium and 2 large spherical charms and each of the 10 charms is uniquely designed. Kitty arranges…
  12. 12How 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?…
  13. 13从11，22，33，44，55这组数据中，随机取出三个不同的数，用XX表示取出的数字的最小数，则随机变量XX的数学期望E(X)=()E(X)=(\quad) A. 32\dfrac{3}{2} B.…
  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. 15The Dragonvale Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of…
  16. 16Twelve students from three CCAs organised an overseas learning trip to Shanghai. It comprises five students from Tennis,…
  17. 17A team of 15 students was selected for an outdoor education trip. One student volunteered to be the trip leader while an…
  18. 18The mass, XX grams, of soup packed into a can by machine AA is normally distributed with mean μ\mu grams and standard…
  19. 19A bakery produces batches of cookies. On average, the proportion of flawed cookies produced is pp, where 0<p<10 < p < 1. T…
  20. 20Section B: Probability and Statistics [60 marks] The basketball club in a college has 5 centers, 8 forwards and 7 guards…
  21. 21平面上有5个点，其中任意三点都不在同一条直线上，则这些点共可组成 个不同的三角形．
  22. 22In a particular year, a company awards scholarships to 4 applicants from a group of nn applicants. If the order of sele…
  23. 23In how many ways can the letters in BEEKEEPERBEEKEEPER be rearranged so that two or more Es do not appear together? A. 1 B. 4 C…
  24. 24The basketball club in a college has 5 centers, 8 forwards and 7 guards. With the National School Games approaching, the…
  25. 25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…
  26. 26A class of twenty-five pupils consists of 15 girls and 10 boys. At the beginning of the year four pupils are to be chose…
  27. 27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
  28. 28An office team of 10 people includes 7 men and 3 women named Anne, Beth, and Cathie. For an upcoming fire drill exercise…
  29. 29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…
  30. 30A small company makes wine glasses. Each day, n randomly chosen wine glasses are checked and the number of wine glasses…
  31. 31In a strategy game called Colour Clash, players draw coloured orbs from a magical pouch to determine their elemental p…
  32. 32A committee consisting of six people is to be selected from five women and six men. Three of the women are sisters. Find…
  33. 33During the Christmas party, five friends sat around a round table in the restaurant with seats labelled 1 to 5. At the N…
  34. 34Makayla finds all the possible ways to draw a path in a 5×55 \times 5 diamond-shaped grid. Each path starts at the bottom…
  35. 35A bag contains 4 red counters and 6 blue counters. 4 counters are drawn from the bag at random, without replacement. Cal…
  36. 36**In this question, you should state clearly all the distributions that you use, together with the values of the appropr…
  37. 37A card game called "Happy Family" is played with 28 cards, consisting of 7 sets of 4 cards. Each set consists of a fathe…
  38. 38A student needs to create a 7-character alpha-numeric passcode (that is, at least one letter and one digit must be inclu…
  39. 39A group of ten people consists of four single women, two single men and 2 couples. The ten people are arranged randomly…
  40. 40A gathering of 12 people break into 3 groups of 4 to play 3 different games: carrom, UNO and bridge. Find the number of…
  41. 41A group of seven people consisting of two single men, three single women and one married couple are arranged to be seate…
  42. 42Five different awards are to be given to three students. Each student will receive at least one award. In how many diffe…
  43. 43学校有88名教师进行象棋比赛，如果每22名教师之间都进行一场比赛，一共要比赛___场．
  44. 44A 6-sided die has three faces marked with a '1', two faces marked with a '2' and one face marked with a '3'. Another 6-s…
  45. 45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))．
  46. 46Given f(r)=r(r−1)!\mathrm{f}(r) = \frac{r}{(r-1)!}, show that f(r−1)−f(r)=r2−3r+1(r−1)!\mathrm{f}(r-1) - \mathrm{f}(r) = \frac{r^2 - 3r + 1}{(r-1)!}.
  47. 47在66盒酸奶中，有22盒已经过了保质期，从中任取22盒，取到的酸奶中有已过保质期的概率为 A. 13\dfrac{1}{3} B. 23\dfrac{2}{3} C. 35\dfrac{3}{5} D. 115\dfrac{1}{15}…
  48. 48The Ang family, the Bao family and the Chew family have three, five and four members respectively. The three families ar…
  49. 49How many integers between 20202020 and 24002400 have four distinct digits arranged in increasing order? (For example, 23472347…
  50. 50Nine gifts, three of which are identical and the rest are distinct, are distributed among five people without restrictio…
  51. 51Find the number of ways in which 4-letter code-words can be obtained from the word ENDANGERED if there are no repeated l…
  52. 52An eatery is giving out free burgers in a promotion to celebrate its anniversary. A total of 80 burgers, consisting of 8…
  53. 53

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

  54. 54Some MRT trains have cars featuring 12 seats each. Passengers take the trains to travel from station to station each day…
  55. 55Two digits XX and YY are chosen independently at random from the set of 10 digits {0, 1, 2, . . . , 9}. Events AA and…
  56. 56From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the pr…
  57. 57How 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?…
  58. 5820222022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))
  59. 59An interest group of 8 members consists of one married couple together with 4 other men and 2 other women. Find the numb…
  60. 6020212021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…