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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 92 · 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.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 28 (d) 16
  2. 2.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  3. 3.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) 30 (b) 20 (c) 8 (d) 15
  4. 4.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 42 (c) 10 (d) 28
  5. 5.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 45 (d) 55
  6. 6.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 72 (d) 36
  7. 7.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  8. 8.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  9. 9.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  10. 10.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 12 (d) 15
  11. 11.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  12. 12.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 60 (b) 11 (c) 35 (d) 30
  13. 13.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 225 (d) 210
  14. 14.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 20 (d) 10
  15. 15.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 21 (c) 25 (d) 10
  16. 16.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 36 (d) 15
  17. 17.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 144 (d) 66
  18. 18.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  19. 19.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 56 (d) 28
  20. 20.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  21. 21.There are 6 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) 36 (b) 30 (c) 11 (d) 60
  22. 22.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 15 (d) 10
  23. 23.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  24. 24.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 72 (d) 81
  25. 25.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  26. 26.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 66 (d) 132
  27. 27.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 182 (c) 196 (d) 91
  28. 28.There are 7 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) 10 (b) 21 (c) 28 (d) 42
  29. 29.There are 6 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) 84 (b) 13 (c) 48 (d) 42
  30. 30.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 78 (c) 169 (d) 156
  31. 31.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 50 (c) 25 (d) 30
  32. 32.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) 70 (b) 35 (c) 42 (d) 12
  33. 33.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  34. 34.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) 56 (c) 28 (d) 11
  35. 35.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 49 (d) 42
  36. 36.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 72 (d) 36
  37. 37.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 30 (c) 48 (d) 10
  38. 38.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
  39. 39.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 66 (d) 24
  40. 40.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 240 (d) 25

Answer key

  1. 28
  2. 24
  3. 15
  4. 21
  5. 45
  6. 36
  7. 24
  8. 6
  9. 24
  10. 15
  11. 24
  12. 30
  13. 105
  14. 10
  15. 20
  16. 15
  17. 66
  18. 120
  19. 28
  20. 24
  21. 30
  22. 10
  23. 120
  24. 36
  25. 120
  26. 132
  27. 91
  28. 21
  29. 42
  30. 78
  31. 25
  32. 35
  33. 6
  34. 28
  35. 42
  36. 72
  37. 24
  38. 21
  39. 66
  40. 120

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