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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 523 · 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 STAR be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  2. 2.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) 8 (b) 20 (c) 32 (d) 16
  3. 3.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 20 (d) 10
  4. 4.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  5. 5.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  6. 6.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 12 (c) 72 (d) 36
  7. 7.8 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) 64 (b) 15 (c) 56 (d) 112
  8. 8.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) 70 (b) 42 (c) 35 (d) 12
  9. 9.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 22 (c) 110 (d) 121
  10. 10.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  11. 11.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 100 (d) 90
  12. 12.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) 9 (b) 40 (c) 25 (d) 20
  13. 13.7 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) 35 (b) 42 (c) 70 (d) 12
  14. 14.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 28 (c) 64 (d) 36
  15. 15.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  16. 16.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 56 (d) 28
  17. 17.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 30 (d) 15
  18. 18.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 182 (d) 105
  19. 19.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 91 (c) 78 (d) 156
  20. 20.There are 8 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 64 (b) 56 (c) 112 (d) 15
  21. 21.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) 7 (b) 24 (c) 12 (d) 15
  22. 22.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
  23. 23.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  24. 24.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) 35 (b) 12 (c) 42 (d) 70
  25. 25.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 81 (d) 45
  26. 26.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) 18 (c) 9 (d) 21
  27. 27.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
  28. 28.3 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
  29. 29.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
  30. 30.4 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) 24 (c) 9 (d) 20
  31. 31.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 55 (d) 66
  32. 32.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 30 (d) 15
  33. 33.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  34. 34.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 42 (d) 21
  35. 35.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 20 (d) 11
  36. 36.3 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) 15 (b) 12 (c) 7 (d) 24
  37. 37.There are 5 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) 8 (b) 30 (c) 15 (d) 20
  38. 38.There are 7 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) 21 (b) 9 (c) 28 (d) 14
  39. 39.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 132 (d) 66
  40. 40.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) 24 (c) 40 (d) 20

Answer key

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

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