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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 527 · 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 7 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 11 (c) 32 (d) 28
  2. 2.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) 8 (c) 16 (d) 6
  3. 3.6 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) 72 (b) 36 (c) 42 (d) 12
  4. 4.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 24 (c) 32 (d) 10
  5. 5.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  6. 6.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 30 (c) 21 (d) 36
  7. 7.5 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) 70 (b) 35 (c) 40 (d) 12
  8. 8.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 45 (c) 36 (d) 81
  9. 9.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 20 (c) 15 (d) 30
  10. 10.5 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) 15 (b) 7 (c) 20 (d) 10
  11. 11.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 64 (c) 28 (d) 36
  12. 12.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  13. 13.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  14. 14.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  15. 15.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  16. 16.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) 36 (d) 30
  17. 17.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 20 (d) 10
  18. 18.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 182 (d) 105
  19. 19.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 78 (c) 169 (d) 91
  20. 20.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 55 (d) 121
  21. 21.7 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) 13 (b) 49 (c) 42 (d) 84
  22. 22.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 196 (d) 105
  23. 23.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) 11 (b) 60 (c) 35 (d) 30
  24. 24.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 64 (b) 40 (c) 12 (d) 32
  25. 25.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 72 (d) 18
  26. 26.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 132 (d) 24
  27. 27.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) 7 (b) 24 (c) 16 (d) 12
  28. 28.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) 56 (b) 11 (c) 28 (d) 35
  29. 29.8 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) 64 (b) 32 (c) 40 (d) 12
  30. 30.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 105 (c) 120 (d) 210
  31. 31.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 30 (d) 15
  32. 32.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 30 (d) 36
  33. 33.There are 4 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) 7 (b) 24 (c) 16 (d) 12
  34. 34.3 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) 15 (b) 24 (c) 12 (d) 7
  35. 35.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) 50 (b) 10 (c) 25 (d) 30
  36. 36.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) 24 (b) 8 (c) 12 (d) 18
  37. 37.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
  38. 38.There are 3 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) 10 (b) 24 (c) 42 (d) 21
  39. 39.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 18 (c) 9 (d) 6
  40. 40.6 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) 48 (b) 10 (c) 24 (d) 30

Answer key

  1. 28
  2. 8
  3. 36
  4. 16
  5. 6
  6. 15
  7. 35
  8. 36
  9. 15
  10. 10
  11. 28
  12. 120
  13. 120
  14. 24
  15. 120
  16. 30
  17. 10
  18. 91
  19. 78
  20. 110
  21. 42
  22. 91
  23. 30
  24. 32
  25. 72
  26. 66
  27. 12
  28. 28
  29. 32
  30. 105
  31. 15
  32. 15
  33. 12
  34. 12
  35. 25
  36. 12
  37. 28
  38. 21
  39. 9
  40. 24

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