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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 756 · 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) 64 (b) 56 (c) 36 (d) 28
  2. 2.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) 11 (b) 30 (c) 35 (d) 60
  3. 3.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 182 (c) 91 (d) 196
  4. 4.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
  5. 5.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 42 (c) 49 (d) 28
  6. 6.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  7. 7.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  8. 8.8 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) 64 (b) 32 (c) 40 (d) 12
  9. 9.7 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) 98 (d) 14
  10. 10.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 81 (d) 36
  11. 11.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) 42 (b) 70 (c) 35 (d) 12
  12. 12.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) 22 (d) 110
  13. 13.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 14 (c) 21 (d) 42
  14. 14.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  15. 15.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 64 (d) 28
  16. 16.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 15 (d) 12
  17. 17.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
  18. 18.3 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) 24 (b) 42 (c) 10 (d) 21
  19. 19.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 45 (d) 36
  20. 20.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 66 (d) 132
  21. 21.4 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) 12 (b) 8 (c) 6 (d) 16
  22. 22.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) 18 (b) 21 (c) 36 (d) 9
  23. 23.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  24. 24.4 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) 32 (b) 16 (c) 20 (d) 8
  25. 25.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  26. 26.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 28 (c) 24 (d) 48
  27. 27.3 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) 12 (b) 7 (c) 24 (d) 15
  28. 28.There are 8 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) 10 (b) 24 (c) 32 (d) 16
  29. 29.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  30. 30.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 144 (c) 78 (d) 132
  31. 31.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 36 (c) 64 (d) 28
  32. 32.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) 25 (b) 40 (c) 20 (d) 9
  33. 33.3 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) 5 (b) 9 (c) 12 (d) 6
  34. 34.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 105 (d) 225
  35. 35.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 49 (d) 42
  36. 36.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) 12 (b) 7 (c) 24 (d) 16
  37. 37.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 91 (c) 169 (d) 78
  38. 38.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  39. 39.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 10 (d) 15
  40. 40.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 24 (d) 16

Answer key

  1. 28
  2. 30
  3. 91
  4. 15
  5. 21
  6. 24
  7. 6
  8. 32
  9. 49
  10. 72
  11. 35
  12. 110
  13. 21
  14. 120
  15. 28
  16. 30
  17. 45
  18. 21
  19. 36
  20. 132
  21. 8
  22. 18
  23. 24
  24. 16
  25. 120
  26. 24
  27. 12
  28. 16
  29. 24
  30. 66
  31. 28
  32. 20
  33. 6
  34. 105
  35. 21
  36. 12
  37. 78
  38. 6
  39. 10
  40. 24

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