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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 845 · 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).

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  1. 1.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) 30 (d) 36
  2. 2.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 56 (d) 28
  3. 3.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) 20 (b) 10 (c) 7 (d) 15
  4. 4.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 55 (d) 110
  5. 5.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 6 (d) 3
  6. 6.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  7. 7.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 21 (d) 49
  8. 8.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 105 (c) 120 (d) 210
  9. 9.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) 12 (b) 70 (c) 35 (d) 40
  10. 10.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 144 (d) 66
  11. 11.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 45 (c) 55 (d) 100
  12. 12.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  13. 13.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 225 (c) 210 (d) 105
  14. 14.3 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) 42 (b) 24 (c) 21 (d) 10
  15. 15.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 10 (c) 15 (d) 20
  16. 16.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  17. 17.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  18. 18.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 64 (d) 36
  19. 19.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 18 (c) 81 (d) 72
  20. 20.There are 8 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) 32 (b) 11 (c) 24 (d) 48
  21. 21.8 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) 96 (b) 56 (c) 48 (d) 14
  22. 22.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 78 (c) 144 (d) 66
  23. 23.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 45 (d) 90
  24. 24.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 42 (d) 21
  25. 25.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 42 (d) 21
  26. 26.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 72 (c) 81 (d) 18
  27. 27.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) 13 (b) 42 (c) 48 (d) 84
  28. 28.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
  29. 29.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  30. 30.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) 36 (b) 60 (c) 30 (d) 11
  31. 31.6 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) 24 (b) 18 (c) 12 (d) 8
  32. 32.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 110 (c) 121 (d) 55
  33. 33.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) 60 (c) 11 (d) 35
  34. 34.4 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) 32 (b) 28 (c) 56 (d) 11
  35. 35.There are 7 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) 21 (b) 9 (c) 14 (d) 28
  36. 36.3 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) 9 (b) 21 (c) 36 (d) 18
  37. 37.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) 7 (b) 16 (c) 12 (d) 24
  38. 38.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 15 (d) 12
  39. 39.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 28 (c) 16 (d) 56
  40. 40.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 12 (c) 70 (d) 35

Answer key

  1. 30
  2. 28
  3. 10
  4. 110
  5. 6
  6. 6
  7. 21
  8. 105
  9. 35
  10. 66
  11. 45
  12. 120
  13. 105
  14. 21
  15. 10
  16. 120
  17. 24
  18. 28
  19. 36
  20. 24
  21. 48
  22. 66
  23. 90
  24. 21
  25. 42
  26. 72
  27. 42
  28. 55
  29. 24
  30. 30
  31. 12
  32. 55
  33. 30
  34. 28
  35. 14
  36. 18
  37. 12
  38. 15
  39. 56
  40. 35

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