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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 46 · 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.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 6 (c) 8 (d) 16
  2. 2.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 91 (d) 182
  3. 3.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 15 (c) 21 (d) 30
  4. 4.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  5. 5.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  6. 6.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 66 (c) 144 (d) 78
  7. 7.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) 7 (b) 12 (c) 16 (d) 24
  8. 8.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 55 (c) 110 (d) 121
  9. 9.7 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) 21 (b) 10 (c) 42 (d) 28
  10. 10.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 81 (c) 36 (d) 45
  11. 11.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  12. 12.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 36 (c) 72 (d) 81
  13. 13.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 21 (d) 28
  14. 14.There are 7 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) 49 (b) 13 (c) 84 (d) 42
  15. 15.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 28 (d) 42
  16. 16.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  17. 17.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) 14 (d) 42
  18. 18.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
  19. 19.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 20 (d) 10
  20. 20.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 55 (c) 121 (d) 110
  21. 21.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 24 (c) 40 (d) 20
  22. 22.8 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) 48 (b) 56 (c) 14 (d) 96
  23. 23.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 91 (d) 105
  24. 24.4 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) 24 (b) 9 (c) 40 (d) 20
  25. 25.There are 8 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) 48 (c) 32 (d) 11
  26. 26.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
  27. 27.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 42 (c) 84 (d) 13
  28. 28.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
  29. 29.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 12 (c) 18 (d) 24
  30. 30.7 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) 56 (b) 28 (c) 11 (d) 35
  31. 31.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  32. 32.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 36 (d) 30
  33. 33.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 10 (c) 15 (d) 25
  34. 34.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  35. 35.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 110 (d) 121
  36. 36.8 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) 32 (b) 16 (c) 10 (d) 24
  37. 37.There are 8 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) 12 (b) 32 (c) 40 (d) 64
  38. 38.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 21 (c) 30 (d) 36
  39. 39.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 25 (d) 15
  40. 40.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56

Answer key

  1. 8
  2. 91
  3. 15
  4. 24
  5. 24
  6. 66
  7. 12
  8. 55
  9. 21
  10. 36
  11. 120
  12. 36
  13. 21
  14. 42
  15. 21
  16. 24
  17. 42
  18. 10
  19. 20
  20. 55
  21. 20
  22. 48
  23. 91
  24. 20
  25. 24
  26. 45
  27. 42
  28. 90
  29. 12
  30. 28
  31. 6
  32. 30
  33. 10
  34. 120
  35. 110
  36. 16
  37. 32
  38. 15
  39. 10
  40. 28

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