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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 67 · 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 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 66 (d) 132
  2. 2.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 28 (d) 56
  3. 3.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) 7 (b) 24 (c) 15 (d) 12
  4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  5. 5.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
  6. 6.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) 110 (d) 22
  7. 7.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) 10 (b) 7 (c) 15 (d) 20
  8. 8.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 21 (d) 49
  9. 9.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
  10. 10.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 56 (d) 28
  11. 11.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  12. 12.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) 12 (b) 36 (c) 72 (d) 42
  13. 13.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 100 (c) 20 (d) 45
  14. 14.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 30 (c) 15 (d) 36
  15. 15.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  16. 16.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) 6 (b) 16 (c) 8 (d) 12
  17. 17.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  18. 18.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 55 (d) 110
  19. 19.There are 6 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) 60 (b) 36 (c) 11 (d) 30
  20. 20.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 100 (d) 45
  21. 21.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) 48 (c) 13 (d) 40
  22. 22.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 30 (d) 12
  23. 23.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 156 (d) 78
  24. 24.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  25. 25.7 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) 42 (b) 70 (c) 12 (d) 35
  26. 26.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 16 (c) 56 (d) 28
  27. 27.5 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) 15 (b) 30 (c) 8 (d) 20
  28. 28.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 225 (c) 105 (d) 210
  29. 29.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 100 (d) 45
  30. 30.There are 5 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) 25 (b) 30 (c) 10 (d) 50
  31. 31.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 36 (c) 18 (d) 81
  32. 32.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
  33. 33.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 11 (c) 25 (d) 20
  34. 34.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  35. 35.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 55 (c) 121 (d) 66
  36. 36.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) 6 (b) 12 (c) 16 (d) 8
  37. 37.11 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
  38. 38.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 100 (d) 55
  39. 39.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 36 (c) 30 (d) 21
  40. 40.3 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) 9 (b) 18 (c) 12 (d) 6

Answer key

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

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