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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 118 · 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 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) 20 (b) 9 (c) 40 (d) 25
  2. 2.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 30 (c) 36 (d) 60
  3. 3.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  5. 5.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
  6. 6.4 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) 11 (b) 56 (c) 28 (d) 32
  7. 7.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 15 (d) 20
  8. 8.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 12 (d) 30
  9. 9.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 144 (d) 132
  10. 10.5 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) 9 (b) 25 (c) 20 (d) 40
  11. 11.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  12. 12.There are 3 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) 24 (b) 12 (c) 15 (d) 7
  13. 13.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 144 (d) 132
  14. 14.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  15. 15.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 81 (c) 72 (d) 36
  16. 16.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 66 (c) 78 (d) 144
  17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  18. 18.There are 7 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) 98 (c) 14 (d) 49
  19. 19.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 182 (c) 91 (d) 105
  20. 20.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) 12 (b) 9 (c) 5 (d) 6
  21. 21.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 55 (d) 110
  22. 22.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) 12 (d) 16
  23. 23.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) 35 (b) 28 (c) 56 (d) 11
  24. 24.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) 12 (b) 70 (c) 42 (d) 35
  25. 25.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 56 (d) 28
  26. 26.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  27. 27.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 66 (d) 144
  28. 28.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  29. 29.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 100 (c) 20 (d) 90
  30. 30.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
  31. 31.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 11 (c) 20 (d) 25
  32. 32.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
  33. 33.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 78 (d) 91
  34. 34.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 210 (c) 120 (d) 225
  35. 35.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  36. 36.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 20 (c) 10 (d) 25
  37. 37.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 28 (d) 56
  38. 38.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 11 (c) 56 (d) 28
  39. 39.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  40. 40.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) 15 (b) 18 (c) 30 (d) 8

Answer key

  1. 20
  2. 30
  3. 24
  4. 6
  5. 105
  6. 28
  7. 10
  8. 30
  9. 132
  10. 20
  11. 6
  12. 12
  13. 66
  14. 120
  15. 36
  16. 66
  17. 24
  18. 49
  19. 91
  20. 6
  21. 110
  22. 12
  23. 28
  24. 35
  25. 28
  26. 120
  27. 66
  28. 120
  29. 45
  30. 15
  31. 10
  32. 36
  33. 78
  34. 105
  35. 6
  36. 20
  37. 56
  38. 28
  39. 120
  40. 15

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