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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 61 · 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. 1.4 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) 12 (c) 7 (d) 24
  2. 2.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  3. 3.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 121 (d) 55
  4. 4.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  5. 5.There are 5 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) 40 (b) 35 (c) 12 (d) 70
  6. 6.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  7. 7.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 49 (d) 21
  8. 8.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 100 (d) 55
  9. 9.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 120 (c) 225 (d) 210
  10. 10.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) 11 (b) 32 (c) 48 (d) 24
  11. 11.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
  12. 12.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 81 (d) 36
  13. 13.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  14. 14.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
  15. 15.There are 5 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) 40 (b) 9 (c) 20 (d) 25
  16. 16.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  17. 17.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  18. 18.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) 24 (b) 18 (c) 9 (d) 36
  19. 19.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  20. 20.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  21. 21.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 132 (d) 24
  22. 22.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
  23. 23.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 110 (c) 55 (d) 66
  24. 24.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 144 (c) 132 (d) 66
  25. 25.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 81 (c) 18 (d) 72
  26. 26.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
  27. 27.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 9 (c) 36 (d) 24
  28. 28.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 11 (c) 56 (d) 32
  29. 29.There are 8 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) 12 (b) 40 (c) 64 (d) 32
  30. 30.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 91 (d) 105
  31. 31.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  32. 32.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 36 (d) 15
  33. 33.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) 24 (b) 20 (c) 40 (d) 9
  34. 34.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 45 (d) 90
  35. 35.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 28 (d) 21
  36. 36.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 55 (c) 110 (d) 121
  37. 37.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 36 (d) 30
  38. 38.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 15 (c) 36 (d) 12
  39. 39.3 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) 18 (b) 30 (c) 15 (d) 8
  40. 40.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 28 (c) 36 (d) 64

Answer key

  1. 12
  2. 24
  3. 55
  4. 24
  5. 35
  6. 24
  7. 21
  8. 45
  9. 105
  10. 24
  11. 12
  12. 36
  13. 6
  14. 6
  15. 20
  16. 120
  17. 120
  18. 18
  19. 24
  20. 6
  21. 66
  22. 15
  23. 55
  24. 66
  25. 72
  26. 10
  27. 18
  28. 28
  29. 32
  30. 91
  31. 120
  32. 15
  33. 20
  34. 45
  35. 21
  36. 110
  37. 30
  38. 15
  39. 15
  40. 28

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