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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 323 · 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 2 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 12 (c) 6 (d) 5
  2. 2.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) 15 (b) 8 (c) 30 (d) 18
  3. 3.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) 80 (b) 13 (c) 40 (d) 48
  4. 4.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 42 (c) 70 (d) 12
  5. 5.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 91 (d) 105
  6. 6.There are 6 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) 48 (b) 84 (c) 42 (d) 13
  7. 7.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) 36 (b) 9 (c) 21 (d) 18
  8. 8.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 24 (c) 12 (d) 16
  9. 9.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 22 (d) 110
  10. 10.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 105 (d) 120
  11. 11.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  12. 12.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 66 (c) 110 (d) 121
  13. 13.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 66 (c) 24 (d) 144
  14. 14.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 36 (c) 64 (d) 56
  15. 15.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) 35 (d) 40
  16. 16.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  17. 17.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 225 (c) 210 (d) 105
  18. 18.There are 7 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) 28 (c) 21 (d) 14
  19. 19.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  20. 20.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 28 (c) 64 (d) 56
  21. 21.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
  22. 22.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  23. 23.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 110 (c) 55 (d) 22
  24. 24.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  25. 25.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) 42 (b) 36 (c) 12 (d) 72
  26. 26.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 36 (d) 81
  27. 27.There are 4 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) 48 (b) 28 (c) 10 (d) 24
  28. 28.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  29. 29.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 10 (c) 20 (d) 25
  30. 30.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 15 (d) 30
  31. 31.3 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) 24 (b) 15 (c) 7 (d) 12
  32. 32.8 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) 96 (d) 14
  33. 33.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
  34. 34.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 49 (c) 42 (d) 28
  35. 35.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 81 (d) 36
  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 team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 66 (d) 24
  38. 38.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 72 (d) 81
  39. 39.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 12 (c) 30 (d) 36
  40. 40.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 25 (c) 20 (d) 15

Answer key

  1. 6
  2. 15
  3. 40
  4. 35
  5. 91
  6. 42
  7. 18
  8. 12
  9. 55
  10. 105
  11. 6
  12. 55
  13. 132
  14. 28
  15. 35
  16. 24
  17. 105
  18. 14
  19. 6
  20. 56
  21. 42
  22. 24
  23. 110
  24. 120
  25. 36
  26. 36
  27. 24
  28. 120
  29. 10
  30. 15
  31. 12
  32. 48
  33. 10
  34. 21
  35. 36
  36. 120
  37. 66
  38. 36
  39. 15
  40. 10

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