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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 629 · 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. 1.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 91 (d) 105
  2. 2.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
  3. 3.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) 32 (b) 10 (c) 24 (d) 16
  4. 4.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  5. 5.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 10 (c) 20 (d) 25
  6. 6.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 55 (c) 110 (d) 121
  7. 7.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 56 (c) 64 (d) 16
  8. 8.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 20 (d) 45
  9. 9.6 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) 12 (b) 8 (c) 18 (d) 24
  10. 10.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) 24 (b) 7 (c) 15 (d) 12
  11. 11.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) 28 (b) 24 (c) 48 (d) 10
  12. 12.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  13. 13.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 16 (c) 56 (d) 64
  14. 14.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 10 (d) 25
  15. 15.There are 5 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) 50 (b) 30 (c) 25 (d) 10
  16. 16.There are 6 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) 42 (b) 36 (c) 72 (d) 12
  17. 17.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 3 (d) 12
  18. 18.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 121 (d) 55
  19. 19.3 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) 9 (b) 6 (c) 5 (d) 12
  20. 20.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  21. 21.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 80 (c) 40 (d) 13
  22. 22.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 36 (d) 30
  23. 23.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 182 (d) 196
  24. 24.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  25. 25.There are 3 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) 10 (b) 42 (c) 21 (d) 24
  26. 26.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 48 (c) 32 (d) 24
  27. 27.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 144 (d) 132
  28. 28.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 66 (d) 144
  29. 29.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 15 (c) 7 (d) 20
  30. 30.8 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
  31. 31.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  32. 32.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 20 (d) 45
  33. 33.8 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
  34. 34.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) 12 (c) 15 (d) 24
  35. 35.7 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) 12 (c) 42 (d) 70
  36. 36.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  37. 37.There are 4 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) 32 (b) 56 (c) 28 (d) 11
  38. 38.There are 5 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) 70 (b) 12 (c) 35 (d) 40
  39. 39.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) 49 (b) 56 (c) 14 (d) 98
  40. 40.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 21 (d) 49

Answer key

  1. 91
  2. 20
  3. 16
  4. 24
  5. 10
  6. 110
  7. 28
  8. 45
  9. 12
  10. 12
  11. 24
  12. 24
  13. 56
  14. 10
  15. 25
  16. 36
  17. 6
  18. 55
  19. 6
  20. 6
  21. 40
  22. 30
  23. 91
  24. 120
  25. 21
  26. 24
  27. 66
  28. 66
  29. 10
  30. 32
  31. 120
  32. 90
  33. 28
  34. 12
  35. 35
  36. 120
  37. 28
  38. 35
  39. 49
  40. 21

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