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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 752 · 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.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 144 (d) 66
  2. 2.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 15 (c) 30 (d) 36
  3. 3.There are 6 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) 72 (b) 42 (c) 36 (d) 12
  4. 4.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 120 (d) 225
  5. 5.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 132 (c) 24 (d) 66
  6. 6.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  7. 7.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 55 (c) 121 (d) 110
  8. 8.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
  9. 9.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  10. 10.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  11. 11.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 49 (c) 42 (d) 28
  12. 12.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) 14 (c) 48 (d) 96
  13. 13.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) 20 (b) 30 (c) 8 (d) 15
  14. 14.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 10 (d) 20
  15. 15.4 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) 32 (b) 11 (c) 56 (d) 28
  16. 16.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 110 (c) 66 (d) 121
  17. 17.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  18. 18.5 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) 8 (b) 20 (c) 30 (d) 15
  19. 19.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 10 (d) 15
  20. 20.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) 16 (b) 24 (c) 12 (d) 7
  21. 21.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  22. 22.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 30 (c) 15 (d) 36
  23. 23.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 90 (d) 55
  24. 24.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  25. 25.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 81 (c) 72 (d) 18
  26. 26.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 21 (c) 25 (d) 10
  27. 27.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  28. 28.8 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) 48 (b) 80 (c) 40 (d) 13
  29. 29.There are 3 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) 10 (b) 42 (c) 24 (d) 21
  30. 30.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  31. 31.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
  32. 32.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) 42 (d) 72
  33. 33.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 30 (d) 12
  34. 34.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  35. 35.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 30 (d) 12
  36. 36.7 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) 14 (b) 98 (c) 56 (d) 49
  37. 37.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 28 (c) 64 (d) 16
  38. 38.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 100 (d) 45
  39. 39.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 78 (d) 132
  40. 40.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 12 (d) 3

Answer key

  1. 66
  2. 15
  3. 36
  4. 105
  5. 132
  6. 120
  7. 55
  8. 21
  9. 24
  10. 24
  11. 21
  12. 48
  13. 15
  14. 10
  15. 28
  16. 55
  17. 24
  18. 15
  19. 10
  20. 12
  21. 120
  22. 15
  23. 45
  24. 24
  25. 36
  26. 20
  27. 120
  28. 40
  29. 21
  30. 120
  31. 72
  32. 36
  33. 30
  34. 24
  35. 15
  36. 49
  37. 56
  38. 45
  39. 66
  40. 6

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