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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 204 · 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).

NameDateTime takenScore ___ / 40
  1. 1.There are 4 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) 9 (b) 20 (c) 40 (d) 24
  2. 2.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 66 (d) 132
  3. 3.3 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) 36 (b) 21 (c) 18 (d) 9
  4. 4.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 21 (d) 14
  5. 5.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 15 (d) 36
  6. 6.6 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 60 (b) 30 (c) 36 (d) 11
  7. 7.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 56 (c) 64 (d) 28
  8. 8.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 91 (d) 156
  9. 9.There are 3 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 18 (c) 21 (d) 36
  10. 10.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 225 (c) 210 (d) 120
  11. 11.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 32 (c) 8 (d) 16
  12. 12.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 9 (c) 28 (d) 14
  13. 13.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 15 (c) 24 (d) 7
  14. 14.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 132 (d) 144
  15. 15.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  16. 16.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 66 (c) 110 (d) 55
  17. 17.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 36 (c) 9 (d) 21
  18. 18.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 42 (c) 28 (d) 21
  19. 19.3 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) 7 (b) 15 (c) 24 (d) 12
  20. 20.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  21. 21.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 10 (c) 15 (d) 20
  22. 22.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 78 (c) 169 (d) 156
  23. 23.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 81 (c) 36 (d) 72
  24. 24.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) 28 (b) 11 (c) 56 (d) 32
  25. 25.There are 3 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) 10 (b) 42 (c) 21 (d) 24
  26. 26.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  27. 27.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  28. 28.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 50 (c) 30 (d) 25
  29. 29.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 48 (c) 96 (d) 56
  30. 30.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 144 (d) 132
  31. 31.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 11 (d) 10
  32. 32.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
  33. 33.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 14 (b) 48 (c) 56 (d) 96
  34. 34.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  35. 35.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 49 (d) 42
  36. 36.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 90 (c) 100 (d) 20
  37. 37.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 182 (c) 196 (d) 91
  38. 38.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 45 (c) 90 (d) 20
  39. 39.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 28 (d) 64
  40. 40.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 12 (d) 30

Answer key

  1. 20
  2. 132
  3. 18
  4. 21
  5. 15
  6. 30
  7. 28
  8. 78
  9. 18
  10. 105
  11. 16
  12. 14
  13. 12
  14. 66
  15. 120
  16. 55
  17. 18
  18. 21
  19. 12
  20. 24
  21. 10
  22. 78
  23. 36
  24. 28
  25. 21
  26. 24
  27. 120
  28. 25
  29. 48
  30. 66
  31. 10
  32. 42
  33. 48
  34. 24
  35. 21
  36. 90
  37. 91
  38. 45
  39. 56
  40. 30

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