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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 693 · 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.There are 8 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) 112 (b) 56 (c) 64 (d) 15
  2. 2.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 49 (c) 42 (d) 28
  3. 3.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  4. 4.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) 16 (b) 24 (c) 12 (d) 7
  5. 5.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 66 (d) 132
  6. 6.8 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) 13 (b) 48 (c) 40 (d) 80
  7. 7.There are 6 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) 24 (c) 18 (d) 8
  8. 8.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 36 (d) 12
  9. 9.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
  10. 10.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
  11. 11.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 55 (c) 22 (d) 121
  12. 12.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 30 (d) 36
  13. 13.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
  14. 14.3 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) 18 (b) 21 (c) 36 (d) 9
  15. 15.8 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) 24 (d) 48
  16. 16.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) 12 (c) 8 (d) 6
  17. 17.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 36 (d) 72
  18. 18.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 210 (c) 225 (d) 120
  19. 19.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 30 (c) 36 (d) 21
  20. 20.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  21. 21.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  22. 22.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 90 (c) 45 (d) 100
  23. 23.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
  24. 24.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 72 (c) 45 (d) 81
  25. 25.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) 42 (c) 36 (d) 72
  26. 26.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) 30 (b) 8 (c) 20 (d) 15
  27. 27.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 56 (c) 36 (d) 28
  28. 28.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 20 (d) 10
  29. 29.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  30. 30.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  31. 31.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) 35 (c) 56 (d) 28
  32. 32.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) 48 (c) 42 (d) 84
  33. 33.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 36 (d) 18
  34. 34.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 55 (c) 90 (d) 45
  35. 35.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) 24 (b) 16 (c) 32 (d) 10
  36. 36.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  37. 37.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  38. 38.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 169 (d) 91
  39. 39.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 55 (d) 110
  40. 40.5 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) 40 (b) 70 (c) 35 (d) 12

Answer key

  1. 56
  2. 21
  3. 24
  4. 12
  5. 66
  6. 40
  7. 12
  8. 15
  9. 56
  10. 55
  11. 110
  12. 30
  13. 105
  14. 18
  15. 24
  16. 8
  17. 36
  18. 105
  19. 15
  20. 24
  21. 120
  22. 90
  23. 21
  24. 36
  25. 36
  26. 15
  27. 28
  28. 10
  29. 6
  30. 6
  31. 28
  32. 42
  33. 36
  34. 45
  35. 16
  36. 120
  37. 120
  38. 78
  39. 55
  40. 35

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