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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 62 · 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 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) 20 (b) 40 (c) 9 (d) 24
  2. 2.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  3. 3.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  4. 4.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) 14 (d) 49
  5. 5.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 11 (c) 24 (d) 32
  6. 6.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 66 (d) 144
  7. 7.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) 20 (b) 8 (c) 16 (d) 32
  8. 8.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 15 (d) 36
  9. 9.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 105 (d) 210
  10. 10.8 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) 14 (b) 48 (c) 96 (d) 56
  11. 11.8 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) 80 (d) 40
  12. 12.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 12 (c) 36 (d) 15
  13. 13.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 64 (d) 28
  14. 14.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 182 (d) 91
  15. 15.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) 9 (b) 21 (c) 14 (d) 28
  16. 16.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) 21 (b) 28 (c) 9 (d) 14
  17. 17.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 55 (d) 90
  18. 18.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) 5 (b) 6 (c) 9 (d) 12
  19. 19.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  20. 20.4 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) 16 (c) 24 (d) 12
  21. 21.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 42 (d) 21
  22. 22.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) 16 (b) 24 (c) 32 (d) 10
  23. 23.4 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) 8 (b) 20 (c) 32 (d) 16
  24. 24.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 121 (d) 66
  25. 25.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 66 (c) 144 (d) 78
  26. 26.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 20 (d) 11
  27. 27.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 156 (c) 169 (d) 78
  28. 28.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) 20 (b) 30 (c) 15 (d) 8
  29. 29.4 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) 10 (b) 48 (c) 28 (d) 24
  30. 30.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) 18 (c) 12 (d) 24
  31. 31.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 20 (d) 90
  32. 32.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 225 (d) 120
  33. 33.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  34. 34.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) 18 (b) 15 (c) 8 (d) 30
  35. 35.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 24 (d) 132
  36. 36.6 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) 84 (b) 42 (c) 13 (d) 48
  37. 37.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 56 (c) 64 (d) 28
  38. 38.There are 5 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) 10 (b) 50 (c) 30 (d) 25
  39. 39.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) 42 (c) 84 (d) 48
  40. 40.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 60 (c) 35 (d) 11

Answer key

  1. 20
  2. 6
  3. 24
  4. 42
  5. 24
  6. 66
  7. 16
  8. 15
  9. 105
  10. 48
  11. 40
  12. 30
  13. 28
  14. 91
  15. 14
  16. 14
  17. 45
  18. 6
  19. 24
  20. 12
  21. 21
  22. 16
  23. 16
  24. 55
  25. 66
  26. 10
  27. 78
  28. 15
  29. 24
  30. 12
  31. 90
  32. 105
  33. 6
  34. 15
  35. 66
  36. 42
  37. 28
  38. 25
  39. 42
  40. 30

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