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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 27 · 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 team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 36 (d) 81
  2. 2.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  3. 3.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) 10 (b) 28 (c) 21 (d) 42
  4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  5. 5.3 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) 42 (b) 21 (c) 10 (d) 24
  6. 6.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 50 (c) 25 (d) 10
  7. 7.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 11 (c) 30 (d) 36
  8. 8.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 36 (c) 28 (d) 64
  9. 9.3 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) 18 (b) 8 (c) 15 (d) 30
  10. 10.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  11. 11.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 25 (c) 20 (d) 15
  12. 12.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 14 (c) 49 (d) 42
  13. 13.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 15 (d) 10
  14. 14.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 90 (d) 100
  15. 15.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 132 (d) 24
  16. 16.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) 18 (d) 6
  17. 17.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 91 (c) 196 (d) 105
  18. 18.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) 56 (d) 14
  19. 19.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 21 (c) 42 (d) 49
  20. 20.There are 3 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) 5 (b) 12 (c) 9 (d) 6
  21. 21.There are 6 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) 36 (c) 60 (d) 11
  22. 22.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  23. 23.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 15 (c) 36 (d) 12
  24. 24.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) 20 (d) 21
  25. 25.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 15 (c) 36 (d) 30
  26. 26.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 210 (c) 105 (d) 225
  27. 27.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  28. 28.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 24 (c) 144 (d) 66
  29. 29.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) 5 (b) 9 (c) 6 (d) 12
  30. 30.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) 24 (b) 48 (c) 32 (d) 11
  31. 31.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) 13 (c) 80 (d) 40
  32. 32.6 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) 48 (b) 13 (c) 42 (d) 84
  33. 33.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  34. 34.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  35. 35.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 45 (c) 81 (d) 36
  36. 36.7 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) 12 (b) 70 (c) 35 (d) 42
  37. 37.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 45 (d) 100
  38. 38.There are 5 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) 9 (b) 20 (c) 25 (d) 40
  39. 39.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
  40. 40.8 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) 48 (b) 32 (c) 11 (d) 24

Answer key

  1. 36
  2. 120
  3. 21
  4. 6
  5. 21
  6. 25
  7. 30
  8. 28
  9. 15
  10. 120
  11. 10
  12. 21
  13. 10
  14. 90
  15. 66
  16. 9
  17. 91
  18. 48
  19. 21
  20. 6
  21. 30
  22. 24
  23. 30
  24. 20
  25. 15
  26. 105
  27. 24
  28. 132
  29. 6
  30. 24
  31. 40
  32. 42
  33. 120
  34. 120
  35. 36
  36. 35
  37. 45
  38. 20
  39. 10
  40. 24

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