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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 81 · 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).

NameDateTime takenScore ___ / 40
  1. 1.6 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) 24 (b) 18 (c) 8 (d) 12
  2. 2.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  3. 3.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) 9 (b) 21 (c) 14 (d) 28
  4. 4.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 30 (c) 35 (d) 60
  5. 5.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  6. 6.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  7. 7.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
  8. 8.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) 110 (d) 55
  9. 9.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) 40 (b) 48 (c) 80 (d) 13
  10. 10.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) 18 (b) 12 (c) 24 (d) 8
  11. 11.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  12. 12.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 20 (c) 40 (d) 24
  13. 13.5 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) 10 (c) 15 (d) 20
  14. 14.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 15 (d) 36
  15. 15.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 84 (c) 49 (d) 42
  16. 16.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 10 (d) 15
  17. 17.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 72 (c) 36 (d) 18
  18. 18.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  19. 19.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 24 (d) 66
  20. 20.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 36 (d) 18
  21. 21.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  22. 22.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  23. 23.There are 4 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) 24 (b) 28 (c) 48 (d) 10
  24. 24.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 55 (c) 121 (d) 110
  25. 25.7 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) 28 (b) 35 (c) 11 (d) 56
  26. 26.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) 12 (c) 24 (d) 15
  27. 27.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 56 (d) 28
  28. 28.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) 7 (c) 15 (d) 12
  29. 29.7 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) 70 (b) 12 (c) 35 (d) 42
  30. 30.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 42 (c) 28 (d) 21
  31. 31.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  32. 32.9 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
  33. 33.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 55 (c) 121 (d) 66
  34. 34.There are 7 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) 12 (b) 35 (c) 42 (d) 70
  35. 35.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  36. 36.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) 24 (b) 40 (c) 20 (d) 9
  37. 37.8 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) 13 (b) 80 (c) 48 (d) 40
  38. 38.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 24 (d) 66
  39. 39.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 49 (d) 28
  40. 40.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 10 (c) 25 (d) 20

Answer key

  1. 12
  2. 120
  3. 14
  4. 30
  5. 120
  6. 120
  7. 15
  8. 110
  9. 40
  10. 12
  11. 24
  12. 20
  13. 10
  14. 15
  15. 42
  16. 10
  17. 72
  18. 24
  19. 66
  20. 36
  21. 6
  22. 120
  23. 24
  24. 55
  25. 28
  26. 12
  27. 28
  28. 12
  29. 35
  30. 21
  31. 6
  32. 36
  33. 55
  34. 35
  35. 6
  36. 20
  37. 40
  38. 132
  39. 21
  40. 10

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