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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 158 · 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) 182 (b) 91 (c) 196 (d) 105
  2. 2.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 16 (d) 56
  3. 3.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 21 (c) 42 (d) 49
  4. 4.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 22 (c) 110 (d) 121
  5. 5.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  6. 6.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  7. 7.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  8. 8.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  9. 9.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 55 (c) 110 (d) 66
  10. 10.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) 21 (c) 42 (d) 24
  11. 11.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) 42 (b) 70 (c) 35 (d) 12
  12. 12.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 20 (c) 100 (d) 45
  13. 13.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15
  14. 14.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) 6 (c) 8 (d) 16
  15. 15.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 49 (d) 42
  16. 16.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) 12 (b) 24 (c) 16 (d) 7
  17. 17.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
  18. 18.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 66 (c) 132 (d) 24
  19. 19.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 56 (c) 36 (d) 28
  20. 20.4 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) 8 (c) 12 (d) 16
  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) 110 (c) 55 (d) 121
  22. 22.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 36 (d) 72
  23. 23.There are 3 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) 18 (b) 8 (c) 15 (d) 30
  24. 24.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 105 (d) 196
  25. 25.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 225 (c) 210 (d) 120
  26. 26.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 30 (d) 36
  27. 27.8 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) 40 (b) 12 (c) 32 (d) 64
  28. 28.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 48 (c) 28 (d) 24
  29. 29.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  30. 30.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) 10 (b) 24 (c) 32 (d) 16
  31. 31.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 144 (d) 132
  32. 32.There are 5 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) 20 (b) 7 (c) 10 (d) 15
  33. 33.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 10 (c) 25 (d) 20
  34. 34.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  35. 35.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  36. 36.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 66 (c) 121 (d) 110
  37. 37.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) 30 (b) 10 (c) 50 (d) 25
  38. 38.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) 48 (d) 84
  39. 39.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
  40. 40.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 12 (c) 30 (d) 36

Answer key

  1. 91
  2. 28
  3. 21
  4. 55
  5. 24
  6. 120
  7. 120
  8. 24
  9. 55
  10. 21
  11. 35
  12. 90
  13. 15
  14. 8
  15. 21
  16. 12
  17. 20
  18. 132
  19. 28
  20. 8
  21. 110
  22. 36
  23. 15
  24. 91
  25. 105
  26. 15
  27. 32
  28. 24
  29. 120
  30. 16
  31. 66
  32. 10
  33. 10
  34. 6
  35. 120
  36. 55
  37. 25
  38. 42
  39. 10
  40. 15

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