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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 225 · 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 3 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) 12 (b) 9 (c) 6 (d) 18
  2. 2.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 30 (d) 15
  3. 3.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 25 (d) 20
  4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  5. 5.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 156 (d) 91
  6. 6.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 182 (d) 105
  7. 7.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 25 (c) 20 (d) 10
  8. 8.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 36 (c) 81 (d) 72
  9. 9.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 45 (d) 20
  10. 10.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 156 (c) 78 (d) 91
  11. 11.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) 60 (b) 30 (c) 35 (d) 11
  12. 12.There are 8 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) 48 (b) 80 (c) 40 (d) 13
  13. 13.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 14 (d) 42
  14. 14.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 132 (d) 66
  15. 15.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 55 (c) 45 (d) 90
  16. 16.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 110 (c) 55 (d) 121
  17. 17.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) 56 (c) 11 (d) 32
  18. 18.4 T-shirts and 2 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) 6 (c) 12 (d) 16
  19. 19.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 70 (c) 40 (d) 35
  20. 20.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
  21. 21.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 132 (d) 144
  22. 22.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 91 (c) 105 (d) 182
  23. 23.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 144 (d) 132
  24. 24.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 21 (c) 10 (d) 28
  25. 25.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) 56 (b) 96 (c) 48 (d) 14
  26. 26.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 18 (b) 6 (c) 12 (d) 9
  27. 27.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 8 (c) 18 (d) 15
  28. 28.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 66 (d) 78
  29. 29.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 10 (d) 20
  30. 30.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 64 (d) 28
  31. 31.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) 16 (b) 12 (c) 7 (d) 24
  32. 32.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  33. 33.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) 9 (b) 21 (c) 36 (d) 18
  34. 34.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 28 (c) 64 (d) 56
  35. 35.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
  36. 36.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  37. 37.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 45 (d) 90
  38. 38.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) 40 (b) 25 (c) 9 (d) 20
  39. 39.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  40. 40.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) 24 (c) 18 (d) 9

Answer key

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

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