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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 761 · 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.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  2. 2.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  3. 3.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 72 (d) 36
  4. 4.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 72 (d) 81
  5. 5.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 45 (d) 81
  6. 6.There are 7 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) 70 (b) 12 (c) 42 (d) 35
  7. 7.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) 16 (b) 8 (c) 20 (d) 32
  8. 8.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 49 (c) 21 (d) 14
  9. 9.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  10. 10.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 36 (c) 18 (d) 72
  11. 11.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) 12 (c) 40 (d) 70
  12. 12.6 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) 11 (b) 30 (c) 60 (d) 36
  13. 13.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 225 (d) 210
  14. 14.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 90 (d) 100
  15. 15.5 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) 11 (b) 35 (c) 60 (d) 30
  16. 16.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) 10 (b) 21 (c) 42 (d) 28
  17. 17.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 30 (d) 36
  18. 18.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 10 (d) 25
  19. 19.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 30 (d) 15
  20. 20.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 36 (c) 64 (d) 28
  21. 21.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 16 (c) 24 (d) 10
  22. 22.4 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) 16 (b) 7 (c) 12 (d) 24
  23. 23.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) 18 (b) 24 (c) 8 (d) 12
  24. 24.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 28 (d) 49
  25. 25.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 36 (c) 9 (d) 18
  26. 26.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 45 (c) 55 (d) 100
  27. 27.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 144 (c) 132 (d) 78
  28. 28.There are 5 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) 15 (b) 20 (c) 8 (d) 30
  29. 29.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 21 (d) 25
  30. 30.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  31. 31.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 36 (c) 64 (d) 28
  32. 32.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 64 (c) 112 (d) 56
  33. 33.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 15 (d) 36
  34. 34.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
  35. 35.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 90 (c) 100 (d) 20
  36. 36.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 21 (c) 49 (d) 14
  37. 37.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  38. 38.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 28 (c) 56 (d) 64
  39. 39.3 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) 12 (b) 9 (c) 5 (d) 6
  40. 40.There are 6 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) 48 (b) 42 (c) 13 (d) 84

Answer key

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

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