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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 819 · 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 a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 36 (d) 30
  2. 2.7 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) 28 (b) 42 (c) 10 (d) 21
  3. 3.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 30 (c) 15 (d) 12
  4. 4.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 66 (c) 110 (d) 121
  5. 5.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 55 (c) 100 (d) 90
  6. 6.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 11 (d) 25
  7. 7.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) 28 (b) 21 (c) 9 (d) 14
  8. 8.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 20 (d) 10
  9. 9.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 20 (d) 45
  10. 10.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  11. 11.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 14 (c) 49 (d) 42
  12. 12.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 105 (c) 182 (d) 196
  13. 13.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 28 (c) 56 (d) 36
  14. 14.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
  15. 15.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 66 (d) 132
  16. 16.3 T-shirts and 4 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) 7 (c) 24 (d) 12
  17. 17.3 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) 21 (b) 24 (c) 42 (d) 10
  18. 18.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) 12 (b) 42 (c) 35 (d) 70
  19. 19.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  20. 20.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 10 (d) 15
  21. 21.There are 7 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) 11 (b) 28 (c) 56 (d) 35
  22. 22.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) 48 (b) 32 (c) 11 (d) 24
  23. 23.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 132 (d) 66
  24. 24.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  25. 25.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  26. 26.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 110 (d) 55
  27. 27.6 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) 48 (b) 42 (c) 84 (d) 13
  28. 28.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 182 (c) 105 (d) 91
  29. 29.8 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) 48 (b) 11 (c) 32 (d) 24
  30. 30.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
  31. 31.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) 8 (b) 20 (c) 16 (d) 32
  32. 32.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 28 (d) 21
  33. 33.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  34. 34.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  35. 35.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  36. 36.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 210 (c) 120 (d) 225
  37. 37.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 20 (d) 45
  38. 38.There are 3 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) 12 (b) 5 (c) 6 (d) 9
  39. 39.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) 56 (b) 11 (c) 32 (d) 28
  40. 40.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) 13 (d) 42

Answer key

  1. 15
  2. 21
  3. 30
  4. 55
  5. 45
  6. 10
  7. 14
  8. 20
  9. 90
  10. 120
  11. 42
  12. 91
  13. 28
  14. 66
  15. 66
  16. 12
  17. 21
  18. 35
  19. 24
  20. 10
  21. 28
  22. 24
  23. 66
  24. 24
  25. 6
  26. 55
  27. 42
  28. 91
  29. 24
  30. 21
  31. 16
  32. 21
  33. 120
  34. 24
  35. 120
  36. 105
  37. 45
  38. 6
  39. 28
  40. 42

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