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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 240 · 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.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  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) 60 (b) 36 (c) 30 (d) 11
  3. 3.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  4. 4.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  5. 5.There are 7 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) 42 (b) 49 (c) 13 (d) 84
  6. 6.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 9 (c) 5 (d) 6
  7. 7.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 66 (c) 55 (d) 121
  8. 8.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 169 (c) 78 (d) 156
  9. 9.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 15 (d) 30
  10. 10.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 56 (c) 64 (d) 16
  11. 11.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  12. 12.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 56 (c) 64 (d) 28
  13. 13.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 15 (c) 21 (d) 36
  14. 14.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) 10 (b) 30 (c) 24 (d) 48
  15. 15.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) 32 (c) 24 (d) 16
  16. 16.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  17. 17.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 20 (d) 15
  18. 18.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
  19. 19.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) 18 (b) 8 (c) 12 (d) 24
  20. 20.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 64 (b) 56 (c) 15 (d) 112
  21. 21.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 7 (c) 15 (d) 10
  22. 22.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 21 (d) 15
  23. 23.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55
  24. 24.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  25. 25.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 49 (d) 21
  26. 26.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  27. 27.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  28. 28.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
  29. 29.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 84 (c) 42 (d) 49
  30. 30.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  31. 31.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 105 (d) 225
  32. 32.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 49 (c) 14 (d) 42
  33. 33.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) 15 (b) 24 (c) 12 (d) 7
  34. 34.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) 9 (b) 25 (c) 40 (d) 20
  35. 35.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 24 (c) 12 (d) 7
  36. 36.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  37. 37.5 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) 20 (c) 25 (d) 40
  38. 38.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) 16 (b) 7 (c) 12 (d) 24
  39. 39.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 36 (c) 21 (d) 18
  40. 40.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) 13 (b) 48 (c) 42 (d) 84

Answer key

  1. 6
  2. 30
  3. 24
  4. 24
  5. 42
  6. 6
  7. 55
  8. 78
  9. 15
  10. 28
  11. 24
  12. 28
  13. 15
  14. 24
  15. 16
  16. 120
  17. 10
  18. 10
  19. 12
  20. 56
  21. 10
  22. 15
  23. 55
  24. 24
  25. 21
  26. 120
  27. 6
  28. 30
  29. 42
  30. 120
  31. 105
  32. 42
  33. 12
  34. 20
  35. 12
  36. 120
  37. 20
  38. 12
  39. 18
  40. 42

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