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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 499 · 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).

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  1. 1.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  2. 2.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  3. 3.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 36 (d) 81
  4. 4.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  5. 5.4 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 40 (c) 9 (d) 20
  6. 6.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) 8 (b) 24 (c) 18 (d) 12
  7. 7.3 T-shirts and 3 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) 12 (c) 6 (d) 18
  8. 8.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  9. 9.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 66 (d) 78
  10. 10.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 182 (c) 105 (d) 91
  11. 11.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 36 (c) 81 (d) 72
  12. 12.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 20 (d) 11
  13. 13.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 28 (d) 21
  14. 14.There are 3 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) 18 (b) 12 (c) 6 (d) 9
  15. 15.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) 20 (d) 40
  16. 16.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  17. 17.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 11 (c) 48 (d) 24
  18. 18.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) 7 (b) 10 (c) 15 (d) 20
  19. 19.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  20. 20.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 28 (d) 49
  21. 21.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 20 (c) 10 (d) 25
  22. 22.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 55 (c) 100 (d) 90
  23. 23.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 66 (d) 144
  24. 24.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 64 (d) 16
  25. 25.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
  26. 26.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 81 (d) 36
  27. 27.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  28. 28.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 110 (d) 55
  29. 29.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  30. 30.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 12 (c) 9 (d) 6
  31. 31.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 90 (d) 100
  32. 32.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) 48 (b) 13 (c) 84 (d) 42
  33. 33.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 91 (c) 78 (d) 169
  34. 34.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 98 (c) 14 (d) 49
  35. 35.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 14 (c) 49 (d) 21
  36. 36.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 121 (c) 55 (d) 110
  37. 37.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  38. 38.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 66 (d) 132
  39. 39.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) 24 (b) 12 (c) 16 (d) 7
  40. 40.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) 40 (c) 35 (d) 70

Answer key

  1. 24
  2. 6
  3. 36
  4. 24
  5. 20
  6. 12
  7. 9
  8. 120
  9. 66
  10. 91
  11. 72
  12. 10
  13. 21
  14. 9
  15. 20
  16. 24
  17. 24
  18. 10
  19. 120
  20. 21
  21. 10
  22. 45
  23. 66
  24. 56
  25. 21
  26. 36
  27. 120
  28. 55
  29. 120
  30. 9
  31. 90
  32. 42
  33. 78
  34. 49
  35. 42
  36. 55
  37. 24
  38. 66
  39. 12
  40. 35

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