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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 621 · 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 a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 25 (d) 20
  2. 2.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  3. 3.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 182 (c) 196 (d) 91
  4. 4.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15
  5. 5.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 78 (c) 156 (d) 169
  6. 6.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) 15 (d) 12
  7. 7.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  8. 8.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) 56 (b) 32 (c) 28 (d) 11
  9. 9.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  10. 10.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 10 (c) 24 (d) 21
  11. 11.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 144 (d) 132
  12. 12.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 110 (c) 121 (d) 22
  13. 13.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
  14. 14.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
  15. 15.There are 3 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) 6 (b) 18 (c) 12 (d) 9
  16. 16.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 16 (c) 24 (d) 12
  17. 17.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 55 (d) 121
  18. 18.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) 25 (c) 40 (d) 20
  19. 19.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 49 (c) 42 (d) 14
  20. 20.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 16 (c) 64 (d) 56
  21. 21.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 64 (b) 112 (c) 56 (d) 15
  22. 22.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  23. 23.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 25 (c) 21 (d) 10
  24. 24.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) 6 (b) 9 (c) 5 (d) 12
  25. 25.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 66 (c) 144 (d) 24
  26. 26.There are 8 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) 32 (b) 24 (c) 48 (d) 11
  27. 27.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  28. 28.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 48 (c) 96 (d) 14
  29. 29.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 120 (c) 225 (d) 210
  30. 30.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  31. 31.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 66 (c) 24 (d) 132
  32. 32.There are 4 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) 7 (b) 24 (c) 16 (d) 12
  33. 33.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) 28 (d) 56
  34. 34.4 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) 32 (b) 20 (c) 8 (d) 16
  35. 35.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 20 (d) 10
  36. 36.5 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) 35 (b) 60 (c) 11 (d) 30
  37. 37.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 169 (c) 78 (d) 156
  38. 38.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 78 (c) 144 (d) 132
  39. 39.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 40 (c) 12 (d) 70
  40. 40.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) 48 (c) 24 (d) 10

Answer key

  1. 10
  2. 24
  3. 91
  4. 15
  5. 78
  6. 30
  7. 24
  8. 28
  9. 120
  10. 21
  11. 66
  12. 55
  13. 12
  14. 21
  15. 9
  16. 12
  17. 110
  18. 20
  19. 42
  20. 28
  21. 56
  22. 6
  23. 20
  24. 6
  25. 66
  26. 24
  27. 24
  28. 48
  29. 105
  30. 24
  31. 132
  32. 12
  33. 56
  34. 16
  35. 10
  36. 30
  37. 78
  38. 66
  39. 35
  40. 24

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