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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 408 · 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, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 30 (c) 15 (d) 36
  2. 2.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 9 (c) 24 (d) 18
  3. 3.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 15 (c) 10 (d) 25
  4. 4.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 42 (c) 21 (d) 14
  5. 5.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 12 (d) 36
  6. 6.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  7. 7.8 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) 14 (b) 56 (c) 96 (d) 48
  8. 8.7 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) 49 (b) 84 (c) 13 (d) 42
  9. 9.There are 8 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) 64 (b) 15 (c) 112 (d) 56
  10. 10.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  11. 11.There are 4 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) 48 (b) 28 (c) 24 (d) 10
  12. 12.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  13. 13.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  14. 14.There are 7 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) 42 (b) 21 (c) 10 (d) 28
  15. 15.6 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) 12 (b) 72 (c) 36 (d) 42
  16. 16.6 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) 12 (c) 24 (d) 18
  17. 17.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 169 (c) 156 (d) 91
  18. 18.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 40 (c) 25 (d) 20
  19. 19.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  20. 20.5 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) 15 (d) 30
  21. 21.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 36 (d) 72
  22. 22.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 20 (d) 25
  23. 23.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 105 (d) 225
  24. 24.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 25 (d) 10
  25. 25.There are 5 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) 60 (b) 30 (c) 35 (d) 11
  26. 26.4 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) 8 (b) 20 (c) 16 (d) 32
  27. 27.There are 7 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) 35 (b) 42 (c) 12 (d) 70
  28. 28.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 81 (d) 72
  29. 29.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 45 (d) 100
  30. 30.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 121 (c) 110 (d) 22
  31. 31.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 132 (d) 144
  32. 32.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) 12 (b) 6 (c) 18 (d) 9
  33. 33.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 210 (d) 225
  34. 34.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 15 (d) 10
  35. 35.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) 18 (b) 24 (c) 8 (d) 12
  36. 36.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 28 (c) 21 (d) 42
  37. 37.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 12 (d) 36
  38. 38.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 20 (d) 45
  39. 39.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 110 (c) 66 (d) 55
  40. 40.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 9 (d) 6

Answer key

  1. 15
  2. 18
  3. 10
  4. 42
  5. 15
  6. 120
  7. 48
  8. 42
  9. 56
  10. 24
  11. 24
  12. 24
  13. 6
  14. 21
  15. 36
  16. 12
  17. 78
  18. 20
  19. 120
  20. 15
  21. 36
  22. 20
  23. 105
  24. 10
  25. 30
  26. 16
  27. 35
  28. 72
  29. 45
  30. 110
  31. 66
  32. 9
  33. 105
  34. 10
  35. 12
  36. 21
  37. 30
  38. 45
  39. 55
  40. 6

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