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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 327 · 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 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) 25 (d) 20
  2. 2.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  3. 3.There are 4 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) 12 (b) 16 (c) 6 (d) 8
  4. 4.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  5. 5.5 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) 11 (b) 35 (c) 30 (d) 60
  6. 6.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) 66 (d) 144
  7. 7.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  8. 8.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
  9. 9.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  10. 10.3 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) 42 (c) 10 (d) 24
  11. 11.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 30 (d) 15
  12. 12.There are 3 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) 21 (b) 9 (c) 18 (d) 36
  13. 13.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 225 (d) 105
  14. 14.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  15. 15.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 156 (c) 78 (d) 169
  16. 16.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 132 (d) 24
  17. 17.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 28 (c) 56 (d) 36
  18. 18.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  19. 19.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  20. 20.14 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
  21. 21.5 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) 7 (b) 20 (c) 10 (d) 15
  22. 22.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 14 (c) 42 (d) 49
  23. 23.There are 6 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) 42 (b) 36 (c) 12 (d) 72
  24. 24.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) 35 (b) 60 (c) 11 (d) 30
  25. 25.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  26. 26.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 144 (c) 132 (d) 78
  27. 27.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 16 (c) 64 (d) 56
  28. 28.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 42 (c) 70 (d) 35
  29. 29.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 182 (c) 91 (d) 105
  30. 30.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 100 (c) 45 (d) 90
  31. 31.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 10 (c) 20 (d) 25
  32. 32.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 15 (c) 24 (d) 12
  33. 33.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 10 (c) 15 (d) 20
  34. 34.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) 16 (b) 24 (c) 12 (d) 7
  35. 35.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) 6 (c) 9 (d) 12
  36. 36.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) 9 (b) 24 (c) 36 (d) 18
  37. 37.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 36 (d) 45
  38. 38.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
  39. 39.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 24 (c) 32 (d) 10
  40. 40.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 36 (d) 15

Answer key

  1. 20
  2. 6
  3. 8
  4. 120
  5. 30
  6. 132
  7. 24
  8. 16
  9. 120
  10. 21
  11. 30
  12. 18
  13. 105
  14. 24
  15. 78
  16. 66
  17. 28
  18. 24
  19. 24
  20. 91
  21. 10
  22. 21
  23. 36
  24. 30
  25. 6
  26. 66
  27. 28
  28. 35
  29. 91
  30. 45
  31. 10
  32. 12
  33. 10
  34. 12
  35. 6
  36. 18
  37. 36
  38. 45
  39. 16
  40. 15

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