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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 536 · 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.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 28 (d) 56
  2. 2.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 21 (c) 49 (d) 42
  3. 3.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  4. 4.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 55 (c) 121 (d) 110
  5. 5.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
  6. 6.There are 3 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 8 (b) 18 (c) 30 (d) 15
  7. 7.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 10 (d) 20
  8. 8.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  9. 9.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  10. 10.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) 60 (d) 30
  11. 11.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 16 (c) 8 (d) 32
  12. 12.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 21 (d) 28
  13. 13.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 105 (c) 196 (d) 182
  14. 14.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 10 (c) 21 (d) 20
  15. 15.8 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) 40 (b) 64 (c) 12 (d) 32
  16. 16.8 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) 80 (b) 40 (c) 48 (d) 13
  17. 17.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 120 (d) 225
  18. 18.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
  19. 19.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  20. 20.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 20 (d) 45
  21. 21.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  22. 22.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 132 (d) 144
  23. 23.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 30 (d) 15
  24. 24.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) 6 (b) 5 (c) 9 (d) 12
  25. 25.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 70 (c) 35 (d) 12
  26. 26.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 40 (c) 80 (d) 13
  27. 27.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 36 (c) 81 (d) 72
  28. 28.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
  29. 29.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 91 (c) 196 (d) 105
  30. 30.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  31. 31.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 55 (c) 66 (d) 121
  32. 32.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 36 (c) 72 (d) 18
  33. 33.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 25 (c) 10 (d) 20
  34. 34.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  35. 35.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  36. 36.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 45 (d) 20
  37. 37.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 55 (d) 121
  38. 38.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 42 (d) 14
  39. 39.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15
  40. 40.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 156 (c) 78 (d) 91

Answer key

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

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