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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 154 · 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.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 15 (c) 12 (d) 36
  2. 2.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
  3. 3.There are 6 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) 36 (b) 9 (c) 18 (d) 24
  4. 4.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) 14 (c) 28 (d) 9
  5. 5.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 78 (c) 169 (d) 91
  6. 6.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 66 (c) 55 (d) 121
  7. 7.3 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) 18 (b) 9 (c) 6 (d) 12
  8. 8.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  9. 9.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  10. 10.4 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) 16 (b) 12 (c) 6 (d) 8
  11. 11.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 91 (c) 105 (d) 196
  12. 12.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 45 (c) 100 (d) 90
  13. 13.6 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
  14. 14.5 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) 25 (b) 20 (c) 40 (d) 9
  15. 15.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 49 (d) 28
  16. 16.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) 36 (b) 9 (c) 21 (d) 18
  17. 17.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 28 (c) 64 (d) 56
  18. 18.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 56 (d) 28
  19. 19.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 30 (d) 15
  20. 20.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 14 (d) 42
  21. 21.4 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) 7 (b) 24 (c) 16 (d) 12
  22. 22.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) 8 (b) 24 (c) 12 (d) 18
  23. 23.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  24. 24.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  25. 25.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 56 (c) 16 (d) 28
  26. 26.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 24 (c) 10 (d) 42
  27. 27.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 120 (c) 210 (d) 225
  28. 28.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 21 (d) 42
  29. 29.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 66 (d) 144
  30. 30.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  31. 31.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 25 (d) 20
  32. 32.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 105 (d) 120
  33. 33.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 55 (c) 121 (d) 110
  34. 34.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 90 (c) 20 (d) 100
  35. 35.There are 5 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) 60 (b) 11 (c) 35 (d) 30
  36. 36.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 11 (d) 20
  37. 37.7 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) 42 (b) 84 (c) 13 (d) 49
  38. 38.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 45 (d) 36
  39. 39.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
  40. 40.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 144 (d) 66

Answer key

  1. 15
  2. 12
  3. 18
  4. 14
  5. 78
  6. 55
  7. 9
  8. 6
  9. 120
  10. 8
  11. 91
  12. 45
  13. 42
  14. 20
  15. 21
  16. 18
  17. 28
  18. 28
  19. 30
  20. 42
  21. 12
  22. 12
  23. 120
  24. 6
  25. 56
  26. 21
  27. 105
  28. 21
  29. 66
  30. 120
  31. 20
  32. 105
  33. 55
  34. 45
  35. 30
  36. 10
  37. 42
  38. 36
  39. 8
  40. 66

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