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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 41 · 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 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) 25 (c) 40 (d) 20
  2. 2.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 28 (d) 64
  3. 3.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 45 (c) 90 (d) 100
  4. 4.There are 6 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) 84 (b) 42 (c) 48 (d) 13
  5. 5.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  6. 6.There are 7 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) 84 (b) 49 (c) 13 (d) 42
  7. 7.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  8. 8.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  9. 9.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 10 (d) 20
  10. 10.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) 30 (b) 18 (c) 8 (d) 15
  11. 11.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 120 (c) 210 (d) 225
  12. 12.5 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
  13. 13.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 182 (c) 196 (d) 91
  14. 14.There are 5 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) 15 (b) 30 (c) 8 (d) 20
  15. 15.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  16. 16.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 132 (c) 144 (d) 24
  17. 17.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 72 (c) 81 (d) 18
  18. 18.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  19. 19.3 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) 24 (b) 12 (c) 7 (d) 15
  20. 20.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  21. 21.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 91 (d) 78
  22. 22.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) 8 (b) 18 (c) 24 (d) 12
  23. 23.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
  24. 24.8 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) 13 (c) 40 (d) 80
  25. 25.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  26. 26.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 6 (c) 8 (d) 16
  27. 27.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 24 (c) 32 (d) 48
  28. 28.3 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) 21 (b) 10 (c) 24 (d) 42
  29. 29.3 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) 9 (b) 18 (c) 6 (d) 12
  30. 30.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 121 (c) 110 (d) 66
  31. 31.6 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) 36 (b) 11 (c) 30 (d) 60
  32. 32.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 42 (c) 49 (d) 21
  33. 33.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) 30 (b) 35 (c) 11 (d) 60
  34. 34.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 182 (d) 196
  35. 35.4 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) 10 (b) 24 (c) 28 (d) 48
  36. 36.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  37. 37.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 55 (d) 45
  38. 38.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
  39. 39.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) 15 (b) 112 (c) 64 (d) 56
  40. 40.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) 35 (b) 28 (c) 56 (d) 11

Answer key

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

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