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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 6 · 40 questions
TalentJR

How to solve it (Multiply the choices): Multiplication principle: a ways for the first choice and b ways for the next give a × b ways together. n different letters in a row: n × (n − 1) × … × 2 × 1 arrangements. Handshakes, matches or teams of 2 from n (order does not matter): n × (n − 1) ÷ 2. Captain and vice-captain (order matters): n × (n − 1).

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  1. 1.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 120 (c) 225 (d) 210
  2. 2.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  3. 3.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 18 (c) 24 (d) 9
  4. 4.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 144 (d) 24
  5. 5.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 42 (c) 49 (d) 28
  6. 6.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 28 (c) 36 (d) 56
  7. 7.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 36 (c) 18 (d) 72
  8. 8.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  9. 9.There are 5 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 70 (b) 35 (c) 40 (d) 12
  10. 10.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 10 (c) 11 (d) 25
  11. 11.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 91 (c) 78 (d) 156
  12. 12.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
  13. 13.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 13 (b) 49 (c) 84 (d) 42
  14. 14.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 49 (c) 42 (d) 14
  15. 15.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
  16. 16.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  17. 17.There are 6 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 60 (b) 36 (c) 30 (d) 11
  18. 18.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 100 (c) 45 (d) 90
  19. 19.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 10 (d) 15
  20. 20.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 66 (d) 132
  21. 21.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 55 (c) 110 (d) 22
  22. 22.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 182 (d) 196
  23. 23.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 15 (d) 21
  24. 24.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  25. 25.There are 5 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 25 (c) 30 (d) 50
  26. 26.There are 4 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 7 (c) 12 (d) 16
  27. 27.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 30 (c) 10 (d) 24
  28. 28.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 72 (c) 36 (d) 42
  29. 29.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  30. 30.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 10 (c) 32 (d) 24
  31. 31.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 91 (c) 156 (d) 169
  32. 32.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 13 (c) 80 (d) 48
  33. 33.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  34. 34.4 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 8 (b) 32 (c) 16 (d) 20
  35. 35.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 28 (c) 11 (d) 56
  36. 36.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 55 (c) 90 (d) 45
  37. 37.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 36 (c) 15 (d) 21
  38. 38.There are 6 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 18 (c) 36 (d) 24
  39. 39.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 6 (c) 5 (d) 12
  40. 40.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 91 (d) 105

Answer key

  1. 105
  2. 120
  3. 18
  4. 66
  5. 21
  6. 28
  7. 36
  8. 6
  9. 35
  10. 10
  11. 78
  12. 36
  13. 42
  14. 42
  15. 45
  16. 120
  17. 30
  18. 45
  19. 10
  20. 132
  21. 110
  22. 91
  23. 15
  24. 6
  25. 25
  26. 12
  27. 24
  28. 36
  29. 24
  30. 16
  31. 78
  32. 40
  33. 120
  34. 16
  35. 28
  36. 45
  37. 15
  38. 18
  39. 6
  40. 91

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