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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 617 · 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 LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  2. 2.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 55 (c) 110 (d) 22
  3. 3.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 72 (d) 18
  4. 4.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  5. 5.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 96 (b) 14 (c) 56 (d) 48
  6. 6.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 132 (d) 24
  7. 7.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  8. 8.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  9. 9.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 16 (c) 56 (d) 64
  10. 10.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 78 (d) 156
  11. 11.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 18 (d) 36
  12. 12.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) 6 (c) 9 (d) 5
  13. 13.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 72 (c) 45 (d) 81
  14. 14.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  15. 15.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 11 (c) 25 (d) 20
  16. 16.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) 7 (b) 12 (c) 24 (d) 15
  17. 17.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 196 (d) 91
  18. 18.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 30 (d) 21
  19. 19.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  20. 20.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) 8 (c) 12 (d) 16
  21. 21.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) 35 (b) 42 (c) 12 (d) 70
  22. 22.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) 25 (b) 10 (c) 30 (d) 50
  23. 23.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 120 (d) 105
  24. 24.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 132 (d) 66
  25. 25.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  26. 26.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) 28 (b) 21 (c) 42 (d) 10
  27. 27.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 182 (d) 91
  28. 28.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 100 (c) 45 (d) 20
  29. 29.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 55 (c) 22 (d) 110
  30. 30.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  31. 31.There are 8 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) 56 (b) 96 (c) 48 (d) 14
  32. 32.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  33. 33.6 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 36 (b) 42 (c) 72 (d) 12
  34. 34.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) 84 (b) 42 (c) 49 (d) 13
  35. 35.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) 28 (b) 56 (c) 11 (d) 35
  36. 36.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 16 (d) 64
  37. 37.5 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) 70 (b) 12 (c) 40 (d) 35
  38. 38.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) 24 (d) 132
  39. 39.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 45 (d) 100
  40. 40.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 48 (d) 24

Answer key

  1. 24
  2. 110
  3. 72
  4. 120
  5. 48
  6. 66
  7. 120
  8. 120
  9. 56
  10. 78
  11. 36
  12. 6
  13. 36
  14. 24
  15. 10
  16. 12
  17. 91
  18. 15
  19. 6
  20. 8
  21. 35
  22. 25
  23. 105
  24. 66
  25. 120
  26. 21
  27. 91
  28. 90
  29. 55
  30. 24
  31. 48
  32. 6
  33. 36
  34. 42
  35. 28
  36. 28
  37. 35
  38. 132
  39. 45
  40. 24

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