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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 165 · 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 6 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 24 (c) 48 (d) 28
  2. 2.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) 60 (b) 30 (c) 35 (d) 11
  3. 3.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 24 (d) 66
  4. 4.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) 24 (b) 16 (c) 12 (d) 7
  5. 5.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 144 (d) 132
  6. 6.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  7. 7.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  8. 8.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) 36 (b) 18 (c) 9 (d) 24
  9. 9.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 72 (c) 81 (d) 45
  10. 10.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 15 (d) 36
  11. 11.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) 12 (b) 8 (c) 24 (d) 18
  12. 12.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  13. 13.There are 3 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) 21 (b) 18 (c) 36 (d) 9
  14. 14.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  15. 15.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 66 (c) 24 (d) 144
  16. 16.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
  17. 17.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) 6 (b) 16 (c) 8 (d) 12
  18. 18.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  19. 19.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 55 (d) 110
  20. 20.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 55 (c) 110 (d) 121
  21. 21.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 121 (c) 110 (d) 66
  22. 22.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) 15 (b) 30 (c) 20 (d) 8
  23. 23.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
  24. 24.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 21 (c) 15 (d) 36
  25. 25.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  26. 26.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 40 (c) 9 (d) 24
  27. 27.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 225 (c) 120 (d) 105
  28. 28.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  29. 29.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  30. 30.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) 10 (b) 21 (c) 42 (d) 28
  31. 31.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) 12 (b) 35 (c) 40 (d) 70
  32. 32.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  33. 33.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 49 (c) 42 (d) 28
  34. 34.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) 35 (c) 70 (d) 42
  35. 35.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 10 (d) 25
  36. 36.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  37. 37.6 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
  38. 38.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 16 (c) 28 (d) 56
  39. 39.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 36 (d) 18
  40. 40.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) 60 (b) 30 (c) 11 (d) 36

Answer key

  1. 24
  2. 30
  3. 66
  4. 12
  5. 66
  6. 24
  7. 6
  8. 18
  9. 36
  10. 15
  11. 12
  12. 120
  13. 18
  14. 120
  15. 132
  16. 30
  17. 8
  18. 24
  19. 55
  20. 55
  21. 55
  22. 15
  23. 12
  24. 15
  25. 6
  26. 20
  27. 105
  28. 6
  29. 24
  30. 21
  31. 35
  32. 24
  33. 21
  34. 35
  35. 10
  36. 24
  37. 15
  38. 56
  39. 36
  40. 30

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