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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 36 · 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 how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  2. 2.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 36 (c) 56 (d) 64
  3. 3.5 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) 40 (b) 35 (c) 12 (d) 70
  4. 4.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  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) 60 (b) 35 (c) 30 (d) 11
  6. 6.8 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) 40 (b) 32 (c) 12 (d) 64
  7. 7.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  8. 8.4 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) 20 (b) 9 (c) 24 (d) 40
  9. 9.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 15 (d) 30
  10. 10.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) 21 (b) 9 (c) 28 (d) 14
  11. 11.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  12. 12.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 28 (d) 42
  13. 13.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 28 (c) 21 (d) 42
  14. 14.3 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
  15. 15.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 20 (d) 25
  16. 16.There are 8 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) 13 (b) 40 (c) 80 (d) 48
  17. 17.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 45 (d) 100
  18. 18.There are 3 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) 24 (b) 15 (c) 7 (d) 12
  19. 19.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 24 (c) 10 (d) 30
  20. 20.4 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) 32 (b) 11 (c) 56 (d) 28
  21. 21.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 55 (d) 110
  22. 22.8 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) 24 (d) 11
  23. 23.4 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) 16 (b) 6 (c) 8 (d) 12
  24. 24.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 36 (d) 45
  25. 25.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 30 (c) 20 (d) 8
  26. 26.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 169 (c) 156 (d) 78
  27. 27.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 72 (d) 36
  28. 28.There are 4 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) 9 (b) 20 (c) 24 (d) 40
  29. 29.There are 6 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) 9 (b) 36 (c) 24 (d) 18
  30. 30.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
  31. 31.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 144 (d) 132
  32. 32.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
  33. 33.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 14 (b) 56 (c) 49 (d) 98
  34. 34.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 30 (c) 12 (d) 15
  35. 35.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 9 (c) 18 (d) 21
  36. 36.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 196 (d) 105
  37. 37.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 132 (d) 144
  38. 38.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  39. 39.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
  40. 40.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 210 (c) 225 (d) 105

Answer key

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

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