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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 702 · 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 5 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 20 (c) 40 (d) 9
  2. 2.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) 24 (b) 7 (c) 15 (d) 12
  3. 3.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 66 (c) 121 (d) 110
  4. 4.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 28 (d) 42
  5. 5.8 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) 56 (b) 14 (c) 96 (d) 48
  6. 6.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
  7. 7.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  8. 8.3 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) 30 (b) 15 (c) 18 (d) 8
  9. 9.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
  10. 10.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  11. 11.6 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) 36 (b) 9 (c) 18 (d) 24
  12. 12.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 11 (c) 48 (d) 32
  13. 13.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  14. 14.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  15. 15.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  16. 16.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 30 (d) 21
  17. 17.There are 6 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) 48 (b) 30 (c) 24 (d) 10
  18. 18.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
  19. 19.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 5 (b) 6 (c) 12 (d) 9
  20. 20.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 132 (d) 24
  21. 21.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 49 (d) 28
  22. 22.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 55 (c) 45 (d) 100
  23. 23.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 16 (d) 28
  24. 24.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 12 (c) 15 (d) 36
  25. 25.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) 18 (b) 30 (c) 8 (d) 15
  26. 26.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 30 (d) 12
  27. 27.5 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) 10 (b) 25 (c) 30 (d) 50
  28. 28.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
  29. 29.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 55 (c) 110 (d) 121
  30. 30.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 84 (b) 13 (c) 49 (d) 42
  31. 31.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 91 (c) 182 (d) 105
  32. 32.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  33. 33.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) 28 (c) 21 (d) 10
  34. 34.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  35. 35.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 25 (c) 50 (d) 10
  36. 36.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 55 (c) 121 (d) 110
  37. 37.3 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) 36 (b) 21 (c) 18 (d) 9
  38. 38.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 105 (d) 182
  39. 39.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) 70 (b) 12 (c) 35 (d) 40
  40. 40.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 36 (c) 81 (d) 18

Answer key

  1. 20
  2. 12
  3. 55
  4. 21
  5. 48
  6. 78
  7. 120
  8. 15
  9. 42
  10. 120
  11. 18
  12. 24
  13. 6
  14. 120
  15. 6
  16. 15
  17. 24
  18. 45
  19. 6
  20. 66
  21. 21
  22. 45
  23. 56
  24. 30
  25. 15
  26. 15
  27. 25
  28. 10
  29. 110
  30. 42
  31. 91
  32. 24
  33. 21
  34. 120
  35. 25
  36. 55
  37. 18
  38. 91
  39. 35
  40. 36

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