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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 89 · 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.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 81 (d) 36
  2. 2.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 156 (c) 169 (d) 78
  3. 3.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 21 (d) 14
  4. 4.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 100 (c) 90 (d) 45
  5. 5.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  6. 6.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 24 (d) 132
  7. 7.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 55 (d) 121
  8. 8.5 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) 12 (b) 35 (c) 70 (d) 40
  9. 9.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  10. 10.3 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) 21 (c) 42 (d) 10
  11. 11.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 105 (c) 120 (d) 225
  12. 12.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  13. 13.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 45 (c) 20 (d) 90
  14. 14.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  15. 15.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  16. 16.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  17. 17.There are 8 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) 80 (b) 48 (c) 13 (d) 40
  18. 18.5 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) 8 (b) 30 (c) 20 (d) 15
  19. 19.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 20 (c) 40 (d) 9
  20. 20.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 10 (d) 15
  21. 21.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 16 (c) 8 (d) 12
  22. 22.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 16 (d) 64
  23. 23.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 55 (d) 110
  24. 24.3 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) 12 (b) 7 (c) 15 (d) 24
  25. 25.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 5 (b) 6 (c) 9 (d) 12
  26. 26.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) 112 (b) 15 (c) 56 (d) 64
  27. 27.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 28 (d) 42
  28. 28.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  29. 29.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 156 (c) 91 (d) 78
  30. 30.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 90 (d) 45
  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) 32 (b) 11 (c) 24 (d) 48
  32. 32.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 144 (c) 78 (d) 132
  33. 33.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 48 (c) 30 (d) 10
  34. 34.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) 35 (c) 40 (d) 12
  35. 35.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  36. 36.3 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) 18 (b) 36 (c) 21 (d) 9
  37. 37.6 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) 42 (b) 48 (c) 84 (d) 13
  38. 38.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) 12 (b) 72 (c) 42 (d) 36
  39. 39.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 21 (d) 28
  40. 40.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 66 (d) 78

Answer key

  1. 72
  2. 78
  3. 21
  4. 45
  5. 24
  6. 66
  7. 55
  8. 35
  9. 6
  10. 21
  11. 105
  12. 24
  13. 90
  14. 120
  15. 120
  16. 120
  17. 40
  18. 15
  19. 20
  20. 10
  21. 8
  22. 28
  23. 55
  24. 12
  25. 6
  26. 56
  27. 21
  28. 24
  29. 78
  30. 45
  31. 24
  32. 66
  33. 24
  34. 35
  35. 120
  36. 18
  37. 42
  38. 36
  39. 21
  40. 66

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