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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 562 · 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 team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 14 (d) 21
  2. 2.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) 20 (b) 25 (c) 40 (d) 9
  3. 3.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 100 (c) 90 (d) 20
  4. 4.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 120 (c) 225 (d) 210
  5. 5.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 121 (c) 22 (d) 110
  6. 6.3 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) 5 (b) 12 (c) 6 (d) 9
  7. 7.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 15 (d) 21
  8. 8.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) 32 (d) 16
  9. 9.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 28 (d) 56
  10. 10.5 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) 25 (b) 40 (c) 9 (d) 20
  11. 11.7 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 98 (b) 56 (c) 49 (d) 14
  12. 12.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 15 (c) 36 (d) 30
  13. 13.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  14. 14.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 48 (c) 28 (d) 10
  15. 15.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 49 (c) 28 (d) 42
  16. 16.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 18 (d) 36
  17. 17.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 30 (d) 15
  18. 18.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 28 (d) 56
  19. 19.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 132 (d) 144
  20. 20.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 8 (c) 20 (d) 16
  21. 21.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  22. 22.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 110 (c) 66 (d) 121
  23. 23.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  24. 24.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 90 (d) 20
  25. 25.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 144 (d) 66
  26. 26.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) 12 (b) 40 (c) 64 (d) 32
  27. 27.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 72 (c) 81 (d) 45
  28. 28.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) 16 (c) 12 (d) 6
  29. 29.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) 16 (b) 7 (c) 12 (d) 24
  30. 30.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 21 (d) 42
  31. 31.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) 24 (b) 15 (c) 12 (d) 7
  32. 32.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  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 LAMP be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  35. 35.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 100 (c) 55 (d) 90
  36. 36.13 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
  37. 37.There are 7 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) 28 (b) 21 (c) 42 (d) 10
  38. 38.3 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) 18 (b) 21 (c) 9 (d) 36
  39. 39.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 42 (c) 14 (d) 49
  40. 40.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 132 (c) 24 (d) 66

Answer key

  1. 21
  2. 20
  3. 45
  4. 105
  5. 110
  6. 6
  7. 15
  8. 16
  9. 28
  10. 20
  11. 49
  12. 30
  13. 120
  14. 24
  15. 21
  16. 36
  17. 15
  18. 28
  19. 66
  20. 16
  21. 120
  22. 55
  23. 6
  24. 90
  25. 66
  26. 32
  27. 36
  28. 8
  29. 12
  30. 21
  31. 12
  32. 120
  33. 10
  34. 24
  35. 45
  36. 78
  37. 21
  38. 18
  39. 42
  40. 132

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