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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 108 · 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 a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 55 (c) 121 (d) 110
  2. 2.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  3. 3.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 55 (d) 90
  4. 4.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  5. 5.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 28 (c) 35 (d) 56
  6. 6.7 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) 70 (b) 35 (c) 42 (d) 12
  7. 7.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  8. 8.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) 12 (b) 9 (c) 6 (d) 18
  9. 9.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 36 (d) 18
  10. 10.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 156 (d) 169
  11. 11.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  12. 12.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 45 (d) 20
  13. 13.5 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) 15 (b) 10 (c) 20 (d) 7
  14. 14.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 42 (d) 21
  15. 15.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 14 (d) 42
  16. 16.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 42 (c) 21 (d) 28
  17. 17.11 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
  18. 18.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 120 (c) 210 (d) 105
  19. 19.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 91 (c) 196 (d) 182
  20. 20.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 56 (d) 64
  21. 21.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 45 (c) 100 (d) 90
  22. 22.3 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) 8 (b) 18 (c) 30 (d) 15
  23. 23.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) 56 (d) 28
  24. 24.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 91 (d) 169
  25. 25.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  26. 26.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) 20 (b) 10 (c) 15 (d) 7
  27. 27.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 132 (d) 66
  28. 28.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  29. 29.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 12 (d) 15
  30. 30.There are 5 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) 25 (b) 10 (c) 50 (d) 30
  31. 31.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  32. 32.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) 56 (b) 48 (c) 96 (d) 14
  33. 33.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 81 (c) 72 (d) 36
  34. 34.6 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) 13 (b) 48 (c) 42 (d) 84
  35. 35.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 15 (d) 20
  36. 36.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  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) 18 (b) 24 (c) 12 (d) 8
  38. 38.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 64 (c) 36 (d) 28
  39. 39.There are 4 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) 7 (b) 12 (c) 24 (d) 16
  40. 40.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10

Answer key

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

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