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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 184 · 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 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 64 (d) 28
  2. 2.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 84 (c) 42 (d) 13
  3. 3.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 12 (c) 16 (d) 24
  4. 4.3 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) 10 (b) 42 (c) 21 (d) 24
  5. 5.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) 7 (b) 10 (c) 20 (d) 15
  6. 6.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 121 (d) 55
  7. 7.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 36 (c) 15 (d) 21
  8. 8.There are 8 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) 32 (b) 16 (c) 24 (d) 10
  9. 9.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 121 (c) 55 (d) 22
  10. 10.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 66 (d) 78
  11. 11.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 10 (c) 15 (d) 25
  12. 12.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 10 (d) 15
  13. 13.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 66 (c) 144 (d) 24
  14. 14.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  15. 15.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 210 (c) 225 (d) 120
  16. 16.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15
  17. 17.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 21 (c) 14 (d) 49
  18. 18.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  19. 19.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 40 (c) 70 (d) 12
  20. 20.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) 32 (b) 56 (c) 11 (d) 28
  21. 21.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 36 (c) 45 (d) 72
  22. 22.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 25 (c) 21 (d) 10
  23. 23.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 28 (d) 42
  24. 24.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  25. 25.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 28 (c) 64 (d) 56
  26. 26.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  27. 27.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 91 (d) 169
  28. 28.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
  29. 29.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  30. 30.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 35 (c) 11 (d) 60
  31. 31.3 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) 6 (b) 9 (c) 18 (d) 12
  32. 32.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  33. 33.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  34. 34.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) 10 (b) 50 (c) 30 (d) 25
  35. 35.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 78 (c) 144 (d) 66
  36. 36.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) 10 (b) 24 (c) 28 (d) 48
  37. 37.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 12 (d) 30
  38. 38.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) 7 (b) 24 (c) 15 (d) 12
  39. 39.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  40. 40.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 121 (d) 55

Answer key

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

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