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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 684 · 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. 1.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 169 (d) 78
  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. 3.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 55 (c) 45 (d) 100
  4. 4.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 36 (c) 72 (d) 81
  5. 5.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 81 (d) 45
  6. 6.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 105 (d) 225
  7. 7.There are 8 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) 32 (b) 64 (c) 40 (d) 12
  8. 8.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 110 (c) 121 (d) 55
  9. 9.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) 8 (b) 18 (c) 12 (d) 24
  10. 10.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  11. 11.There are 6 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) 13 (b) 48 (c) 42 (d) 84
  12. 12.There are 6 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) 9 (b) 24 (c) 36 (d) 18
  13. 13.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 25 (c) 10 (d) 20
  14. 14.There are 7 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) 35 (b) 56 (c) 11 (d) 28
  15. 15.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  16. 16.8 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) 112 (b) 15 (c) 56 (d) 64
  17. 17.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 91 (c) 169 (d) 156
  18. 18.There are 3 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) 15 (b) 18 (c) 30 (d) 8
  19. 19.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 105 (d) 91
  20. 20.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 144 (d) 132
  21. 21.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  22. 22.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) 48 (b) 24 (c) 11 (d) 32
  23. 23.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 15 (d) 36
  24. 24.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  25. 25.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 8 (c) 20 (d) 32
  26. 26.3 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) 8 (b) 30 (c) 15 (d) 18
  27. 27.There are 5 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) 15 (b) 10 (c) 20 (d) 7
  28. 28.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  29. 29.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  30. 30.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 36 (d) 72
  31. 31.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) 48 (b) 24 (c) 11 (d) 32
  32. 32.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 55 (d) 90
  33. 33.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 15 (d) 10
  34. 34.6 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) 12 (b) 36 (c) 42 (d) 72
  35. 35.4 T-shirts and 3 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) 7 (c) 16 (d) 24
  36. 36.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 91 (d) 182
  37. 37.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 30 (d) 15
  38. 38.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) 13 (c) 80 (d) 40
  39. 39.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) 36 (c) 60 (d) 30
  40. 40.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 24 (c) 12 (d) 8

Answer key

  1. 78
  2. 24
  3. 45
  4. 36
  5. 36
  6. 105
  7. 32
  8. 55
  9. 12
  10. 24
  11. 42
  12. 18
  13. 10
  14. 28
  15. 6
  16. 56
  17. 78
  18. 15
  19. 91
  20. 66
  21. 120
  22. 24
  23. 15
  24. 24
  25. 16
  26. 15
  27. 10
  28. 120
  29. 120
  30. 72
  31. 24
  32. 45
  33. 10
  34. 36
  35. 12
  36. 91
  37. 15
  38. 40
  39. 30
  40. 12

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