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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 4 · 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.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  2. 2.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) 12 (b) 6 (c) 5 (d) 9
  3. 3.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) 10 (b) 24 (c) 16 (d) 32
  4. 4.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 55 (d) 121
  5. 5.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  6. 6.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  7. 7.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 28 (d) 64
  8. 8.6 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) 24 (b) 30 (c) 48 (d) 10
  9. 9.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 21 (c) 30 (d) 36
  10. 10.8 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) 40 (c) 48 (d) 80
  11. 11.6 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) 30 (b) 60 (c) 11 (d) 36
  12. 12.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 45 (c) 100 (d) 20
  13. 13.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 28 (c) 49 (d) 42
  14. 14.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 132 (d) 144
  15. 15.8 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) 12 (b) 64 (c) 32 (d) 40
  16. 16.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 91 (d) 169
  17. 17.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 21 (d) 42
  18. 18.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) 21 (c) 28 (d) 42
  19. 19.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 132 (c) 66 (d) 78
  20. 20.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 3 (d) 12
  21. 21.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  22. 22.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 15 (c) 25 (d) 10
  23. 23.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 90 (d) 45
  24. 24.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 144 (d) 66
  25. 25.5 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) 15 (b) 10 (c) 7 (d) 20
  26. 26.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) 11 (b) 60 (c) 30 (d) 36
  27. 27.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) 36 (d) 18
  28. 28.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) 28 (b) 24 (c) 48 (d) 10
  29. 29.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 105 (c) 91 (d) 196
  30. 30.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 36 (c) 18 (d) 81
  31. 31.4 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) 40 (b) 9 (c) 24 (d) 20
  32. 32.4 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) 16 (b) 32 (c) 20 (d) 8
  33. 33.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 55 (d) 45
  34. 34.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 55 (c) 121 (d) 110
  35. 35.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 12 (d) 15
  36. 36.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
  37. 37.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  38. 38.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  39. 39.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  40. 40.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 28 (c) 56 (d) 11

Answer key

  1. 6
  2. 6
  3. 16
  4. 55
  5. 24
  6. 24
  7. 56
  8. 24
  9. 15
  10. 40
  11. 30
  12. 45
  13. 21
  14. 132
  15. 32
  16. 78
  17. 42
  18. 21
  19. 66
  20. 6
  21. 120
  22. 10
  23. 90
  24. 66
  25. 10
  26. 30
  27. 18
  28. 24
  29. 91
  30. 36
  31. 20
  32. 16
  33. 45
  34. 55
  35. 15
  36. 55
  37. 6
  38. 24
  39. 24
  40. 28

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