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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 130 · 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. 1.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 182 (d) 91
  2. 2.There are 8 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) 48 (b) 56 (c) 14 (d) 96
  3. 3.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  4. 4.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 25 (d) 20
  5. 5.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) 72 (c) 36 (d) 42
  6. 6.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 10 (d) 20
  7. 7.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 112 (c) 15 (d) 64
  8. 8.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  9. 9.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 45 (d) 100
  10. 10.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 49 (d) 21
  11. 11.8 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) 56 (b) 48 (c) 14 (d) 96
  12. 12.5 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) 35 (b) 60 (c) 30 (d) 11
  13. 13.5 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) 25 (b) 30 (c) 50 (d) 10
  14. 14.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 10 (d) 11
  15. 15.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 110 (c) 22 (d) 121
  16. 16.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
  17. 17.4 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) 6 (b) 12 (c) 8 (d) 16
  18. 18.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  19. 19.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 10 (c) 20 (d) 25
  20. 20.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  21. 21.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 30 (c) 18 (d) 15
  22. 22.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) 42 (b) 70 (c) 35 (d) 12
  23. 23.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 36 (d) 72
  24. 24.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 36 (d) 72
  25. 25.3 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) 6 (b) 18 (c) 12 (d) 9
  26. 26.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) 35 (b) 70 (c) 42 (d) 12
  27. 27.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) 6 (d) 8
  28. 28.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 21 (c) 49 (d) 14
  29. 29.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 78 (c) 91 (d) 156
  30. 30.There are 7 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) 42 (b) 10 (c) 28 (d) 21
  31. 31.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 15 (c) 7 (d) 12
  32. 32.4 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) 16 (b) 24 (c) 12 (d) 7
  33. 33.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 81 (c) 72 (d) 45
  34. 34.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 66 (c) 78 (d) 132
  35. 35.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) 32 (c) 28 (d) 11
  36. 36.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 98 (c) 49 (d) 14
  37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  38. 38.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 30 (c) 15 (d) 21
  39. 39.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  40. 40.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

Answer key

  1. 91
  2. 48
  3. 24
  4. 20
  5. 36
  6. 10
  7. 56
  8. 6
  9. 45
  10. 21
  11. 48
  12. 30
  13. 25
  14. 10
  15. 110
  16. 30
  17. 8
  18. 120
  19. 10
  20. 24
  21. 15
  22. 35
  23. 36
  24. 36
  25. 9
  26. 35
  27. 8
  28. 42
  29. 78
  30. 21
  31. 12
  32. 12
  33. 36
  34. 66
  35. 28
  36. 49
  37. 120
  38. 15
  39. 6
  40. 55

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