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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 267 · 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) 70 (d) 35
  2. 2.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 15 (c) 21 (d) 36
  3. 3.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
  4. 4.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 21 (d) 42
  5. 5.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) 12 (c) 8 (d) 6
  6. 6.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) 15 (b) 56 (c) 112 (d) 64
  7. 7.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  8. 8.4 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) 10 (b) 48 (c) 28 (d) 24
  9. 9.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) 8 (b) 6 (c) 16 (d) 12
  10. 10.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
  11. 11.There are 4 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) 11 (b) 28 (c) 32 (d) 56
  12. 12.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  13. 13.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) 15 (b) 24 (c) 7 (d) 12
  14. 14.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 12 (d) 30
  15. 15.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 12 (d) 30
  16. 16.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) 20 (c) 9 (d) 25
  17. 17.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 45 (d) 81
  18. 18.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  19. 19.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
  20. 20.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
  21. 21.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  22. 22.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 64 (c) 28 (d) 56
  23. 23.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  24. 24.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 45 (c) 20 (d) 90
  25. 25.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 11 (c) 20 (d) 25
  26. 26.5 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) 15 (b) 20 (c) 10 (d) 7
  27. 27.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 9 (c) 18 (d) 12
  28. 28.11 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
  29. 29.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  30. 30.3 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) 12 (c) 7 (d) 15
  31. 31.There are 7 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) 98 (b) 49 (c) 14 (d) 56
  32. 32.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) 9 (b) 36 (c) 24 (d) 18
  33. 33.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 91 (d) 196
  34. 34.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 105 (c) 210 (d) 120
  35. 35.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) 6 (b) 5 (c) 9 (d) 12
  36. 36.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 24 (c) 144 (d) 66
  37. 37.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 20 (d) 10
  38. 38.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  39. 39.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 110 (c) 55 (d) 121
  40. 40.4 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) 24 (b) 7 (c) 16 (d) 12

Answer key

  1. 35
  2. 15
  3. 90
  4. 21
  5. 8
  6. 56
  7. 24
  8. 24
  9. 8
  10. 36
  11. 28
  12. 24
  13. 12
  14. 30
  15. 15
  16. 20
  17. 36
  18. 120
  19. 105
  20. 21
  21. 6
  22. 28
  23. 6
  24. 45
  25. 10
  26. 10
  27. 9
  28. 55
  29. 24
  30. 12
  31. 49
  32. 18
  33. 91
  34. 105
  35. 6
  36. 132
  37. 10
  38. 120
  39. 55
  40. 12

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