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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 182 · 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, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 56 (c) 64 (d) 36
  2. 2.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 28 (d) 21
  3. 3.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  4. 4.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 35 (c) 28 (d) 11
  5. 5.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 21 (c) 42 (d) 24
  6. 6.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
  7. 7.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
  8. 8.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 55 (d) 66
  9. 9.There are 4 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 32 (c) 16 (d) 8
  10. 10.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
  11. 11.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 49 (d) 21
  12. 12.8 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) 12 (b) 32 (c) 40 (d) 64
  13. 13.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 30 (d) 36
  14. 14.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) 12 (b) 8 (c) 18 (d) 24
  15. 15.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 16 (d) 64
  16. 16.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) 15 (c) 7 (d) 10
  17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  18. 18.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 36 (d) 72
  19. 19.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 16 (d) 64
  20. 20.6 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) 24 (b) 8 (c) 12 (d) 18
  21. 21.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  22. 22.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 144 (c) 78 (d) 132
  23. 23.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 91 (c) 156 (d) 78
  24. 24.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 156 (c) 91 (d) 78
  25. 25.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) 96 (b) 48 (c) 14 (d) 56
  26. 26.There are 8 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) 48 (b) 11 (c) 24 (d) 32
  27. 27.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 10 (d) 20
  28. 28.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  29. 29.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 78 (d) 66
  30. 30.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  31. 31.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
  32. 32.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) 60 (b) 11 (c) 30 (d) 35
  33. 33.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 10 (c) 15 (d) 20
  34. 34.5 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) 20 (b) 15 (c) 7 (d) 10
  35. 35.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  36. 36.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  37. 37.7 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) 49 (b) 56 (c) 14 (d) 98
  38. 38.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  39. 39.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 14 (b) 21 (c) 9 (d) 28
  40. 40.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 121 (c) 22 (d) 55

Answer key

  1. 28
  2. 21
  3. 120
  4. 28
  5. 21
  6. 30
  7. 66
  8. 55
  9. 16
  10. 10
  11. 21
  12. 32
  13. 15
  14. 12
  15. 56
  16. 10
  17. 24
  18. 36
  19. 28
  20. 12
  21. 120
  22. 66
  23. 78
  24. 78
  25. 48
  26. 24
  27. 10
  28. 24
  29. 66
  30. 6
  31. 132
  32. 30
  33. 10
  34. 10
  35. 120
  36. 6
  37. 49
  38. 24
  39. 14
  40. 110

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