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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 32 · 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 4 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 8 (c) 16 (d) 32
  2. 2.3 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) 15 (b) 18 (c) 30 (d) 8
  3. 3.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 169 (d) 91
  4. 4.6 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) 18 (b) 24 (c) 8 (d) 12
  5. 5.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  6. 6.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) 40 (c) 20 (d) 24
  7. 7.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  8. 8.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
  9. 9.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 21 (d) 14
  10. 10.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) 12 (b) 15 (c) 24 (d) 7
  11. 11.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 144 (d) 24
  12. 12.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 49 (d) 28
  13. 13.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 16 (c) 10 (d) 32
  14. 14.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 100 (c) 90 (d) 45
  15. 15.There are 3 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) 30 (b) 15 (c) 8 (d) 18
  16. 16.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 225 (d) 210
  17. 17.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  18. 18.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  19. 19.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 36 (d) 12
  20. 20.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  21. 21.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 121 (c) 22 (d) 55
  22. 22.There are 5 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) 7 (b) 10 (c) 20 (d) 15
  23. 23.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) 18 (c) 8 (d) 15
  24. 24.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 64 (b) 40 (c) 12 (d) 32
  25. 25.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 20 (c) 21 (d) 10
  26. 26.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 7 (c) 10 (d) 20
  27. 27.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 64 (d) 16
  28. 28.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  29. 29.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 20 (d) 45
  30. 30.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 78 (c) 156 (d) 169
  31. 31.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 14 (c) 49 (d) 21
  32. 32.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 66 (d) 132
  33. 33.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  34. 34.There are 4 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) 16 (b) 8 (c) 12 (d) 6
  35. 35.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 15 (c) 36 (d) 30
  36. 36.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) 24 (b) 8 (c) 18 (d) 12
  37. 37.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  38. 38.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 81 (c) 18 (d) 72
  39. 39.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) 21 (c) 28 (d) 14
  40. 40.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 120 (d) 240

Answer key

  1. 16
  2. 15
  3. 78
  4. 12
  5. 24
  6. 20
  7. 24
  8. 110
  9. 21
  10. 12
  11. 66
  12. 21
  13. 16
  14. 45
  15. 15
  16. 105
  17. 120
  18. 120
  19. 30
  20. 24
  21. 55
  22. 10
  23. 15
  24. 32
  25. 20
  26. 10
  27. 56
  28. 6
  29. 90
  30. 78
  31. 42
  32. 66
  33. 6
  34. 8
  35. 15
  36. 12
  37. 120
  38. 72
  39. 14
  40. 120

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