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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 389 · 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 FISH be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  2. 2.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 28 (d) 64
  3. 3.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
  4. 4.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) 7 (b) 15 (c) 10 (d) 20
  5. 5.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 36 (d) 45
  6. 6.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  7. 7.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 132 (d) 144
  8. 8.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 20 (d) 10
  9. 9.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 90 (c) 45 (d) 100
  10. 10.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 121 (c) 55 (d) 110
  11. 11.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 36 (d) 64
  12. 12.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 12 (d) 30
  13. 13.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  14. 14.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 105 (c) 210 (d) 120
  15. 15.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 105 (c) 91 (d) 182
  16. 16.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 15 (c) 12 (d) 36
  17. 17.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 36 (d) 81
  18. 18.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  19. 19.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 36 (c) 72 (d) 42
  20. 20.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) 21 (d) 49
  21. 21.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  22. 22.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  23. 23.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) 11 (b) 35 (c) 30 (d) 60
  24. 24.6 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 8 (b) 24 (c) 18 (d) 12
  25. 25.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 5 (b) 12 (c) 9 (d) 6
  26. 26.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
  27. 27.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 81 (d) 36
  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) 20 (c) 45 (d) 100
  29. 29.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 49 (c) 28 (d) 42
  30. 30.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  31. 31.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 110 (c) 121 (d) 22
  32. 32.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 10 (c) 25 (d) 15
  33. 33.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
  34. 34.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) 15 (b) 20 (c) 8 (d) 30
  35. 35.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 105 (c) 91 (d) 182
  36. 36.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 30 (d) 15
  37. 37.There are 6 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) 8 (b) 12 (c) 24 (d) 18
  38. 38.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 144 (d) 66
  39. 39.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 21 (d) 28
  40. 40.7 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) 42 (b) 84 (c) 49 (d) 13

Answer key

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

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