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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 537 · 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 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) 40 (b) 12 (c) 35 (d) 70
  2. 2.There are 5 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 25 (c) 40 (d) 20
  3. 3.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  4. 4.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 36 (c) 64 (d) 56
  5. 5.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 11 (d) 20
  6. 6.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 120 (d) 105
  7. 7.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 11 (c) 32 (d) 56
  8. 8.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 42 (c) 24 (d) 21
  9. 9.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  10. 10.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) 24 (b) 30 (c) 48 (d) 10
  11. 11.There are 3 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 12 (c) 15 (d) 7
  12. 12.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  13. 13.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  14. 14.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 28 (d) 21
  15. 15.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 30 (d) 21
  16. 16.There are 5 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) 11 (b) 60 (c) 35 (d) 30
  17. 17.3 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) 12 (b) 24 (c) 15 (d) 7
  18. 18.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  19. 19.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 18 (c) 36 (d) 81
  20. 20.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 11 (b) 35 (c) 28 (d) 56
  21. 21.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 10 (c) 25 (d) 20
  22. 22.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 55 (c) 121 (d) 66
  23. 23.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 156 (d) 78
  24. 24.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 21 (c) 25 (d) 10
  25. 25.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 55 (c) 90 (d) 45
  26. 26.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 24 (c) 32 (d) 48
  27. 27.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 55 (c) 45 (d) 100
  28. 28.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 81 (d) 36
  29. 29.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) 48 (c) 13 (d) 80
  30. 30.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 66 (c) 55 (d) 110
  31. 31.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  32. 32.There are 4 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 8 (b) 16 (c) 20 (d) 32
  33. 33.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 9 (c) 5 (d) 12
  34. 34.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  35. 35.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) 7 (b) 15 (c) 12 (d) 24
  36. 36.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 21 (c) 49 (d) 14
  37. 37.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 112 (c) 15 (d) 64
  38. 38.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 225 (c) 210 (d) 105
  39. 39.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 56 (d) 28
  40. 40.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 81 (c) 45 (d) 72

Answer key

  1. 35
  2. 20
  3. 120
  4. 28
  5. 10
  6. 105
  7. 28
  8. 21
  9. 24
  10. 24
  11. 12
  12. 6
  13. 24
  14. 21
  15. 15
  16. 30
  17. 12
  18. 120
  19. 72
  20. 28
  21. 10
  22. 55
  23. 78
  24. 20
  25. 45
  26. 24
  27. 45
  28. 36
  29. 40
  30. 55
  31. 120
  32. 16
  33. 6
  34. 24
  35. 12
  36. 21
  37. 56
  38. 105
  39. 28
  40. 36

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