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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 16 · 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. 1.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 78 (d) 132
  2. 2.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 15 (d) 30
  3. 3.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 10 (c) 25 (d) 20
  4. 4.8 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) 112 (b) 64 (c) 56 (d) 15
  5. 5.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 66 (c) 144 (d) 24
  6. 6.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 45 (c) 90 (d) 100
  7. 7.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) 16 (b) 32 (c) 20 (d) 8
  8. 8.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 42 (d) 21
  9. 9.4 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) 10 (b) 48 (c) 28 (d) 24
  10. 10.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 110 (d) 22
  11. 11.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
  12. 12.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) 11 (b) 30 (c) 60 (d) 36
  13. 13.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  14. 14.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 21 (c) 30 (d) 36
  15. 15.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 36 (d) 81
  16. 16.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  17. 17.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 91 (c) 196 (d) 105
  18. 18.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  19. 19.3 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) 30 (b) 8 (c) 15 (d) 18
  20. 20.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 45 (c) 81 (d) 36
  21. 21.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10
  22. 22.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  23. 23.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 15 (d) 25
  24. 24.There are 6 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 42 (c) 72 (d) 36
  25. 25.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) 16 (b) 6 (c) 12 (d) 8
  26. 26.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  27. 27.6 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) 36 (b) 12 (c) 72 (d) 42
  28. 28.5 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) 30 (b) 20 (c) 15 (d) 8
  29. 29.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  30. 30.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 66 (c) 121 (d) 110
  31. 31.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
  32. 32.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
  33. 33.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
  34. 34.8 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) 32 (b) 11 (c) 48 (d) 24
  35. 35.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  36. 36.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 6 (c) 12 (d) 18
  37. 37.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 84 (b) 13 (c) 42 (d) 49
  38. 38.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 28 (c) 64 (d) 16
  39. 39.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 96 (c) 48 (d) 14
  40. 40.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

Answer key

  1. 66
  2. 15
  3. 10
  4. 56
  5. 66
  6. 45
  7. 16
  8. 21
  9. 24
  10. 55
  11. 90
  12. 30
  13. 6
  14. 15
  15. 36
  16. 120
  17. 91
  18. 120
  19. 15
  20. 36
  21. 10
  22. 120
  23. 10
  24. 36
  25. 8
  26. 24
  27. 36
  28. 15
  29. 120
  30. 55
  31. 36
  32. 15
  33. 28
  34. 24
  35. 24
  36. 9
  37. 42
  38. 56
  39. 48
  40. 30

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