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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 695 · 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).

NameDateTime takenScore ___ / 40
  1. 1.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) 28 (b) 35 (c) 11 (d) 56
  2. 2.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 210 (c) 105 (d) 225
  3. 3.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) 12 (b) 16 (c) 8 (d) 6
  4. 4.6 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) 13 (b) 48 (c) 84 (d) 42
  5. 5.8 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) 80 (b) 40 (c) 13 (d) 48
  6. 6.4 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) 11 (b) 56 (c) 32 (d) 28
  7. 7.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 10 (c) 11 (d) 25
  8. 8.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 21 (d) 14
  9. 9.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
  10. 10.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
  11. 11.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
  12. 12.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  13. 13.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 9 (c) 28 (d) 14
  14. 14.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 28 (c) 49 (d) 42
  15. 15.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 55 (d) 45
  16. 16.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 12 (d) 15
  17. 17.There are 5 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) 10 (b) 20 (c) 7 (d) 15
  18. 18.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 42 (c) 21 (d) 14
  19. 19.8 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) 64 (b) 56 (c) 15 (d) 112
  20. 20.There are 3 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) 9 (b) 36 (c) 21 (d) 18
  21. 21.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 36 (c) 72 (d) 18
  22. 22.8 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
  23. 23.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 20 (d) 25
  24. 24.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) 12 (b) 42 (c) 70 (d) 35
  25. 25.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 36 (d) 81
  26. 26.5 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) 20 (b) 9 (c) 40 (d) 25
  27. 27.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 36 (c) 72 (d) 81
  28. 28.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  29. 29.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  30. 30.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) 32 (b) 11 (c) 28 (d) 56
  31. 31.7 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
  32. 32.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 30 (d) 15
  33. 33.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 91 (c) 169 (d) 156
  34. 34.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
  35. 35.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 15 (d) 21
  36. 36.There are 4 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) 40 (b) 24 (c) 9 (d) 20
  37. 37.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 64 (d) 28
  38. 38.12 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
  39. 39.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  40. 40.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 240 (d) 25

Answer key

  1. 28
  2. 105
  3. 8
  4. 42
  5. 40
  6. 28
  7. 10
  8. 21
  9. 6
  10. 45
  11. 30
  12. 120
  13. 14
  14. 21
  15. 45
  16. 15
  17. 10
  18. 42
  19. 56
  20. 18
  21. 36
  22. 28
  23. 10
  24. 35
  25. 36
  26. 20
  27. 72
  28. 24
  29. 120
  30. 28
  31. 21
  32. 15
  33. 78
  34. 78
  35. 15
  36. 20
  37. 56
  38. 66
  39. 24
  40. 120

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