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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 403 · 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 team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 110 (d) 55
  2. 2.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 64 (c) 28 (d) 36
  3. 3.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) 15 (b) 7 (c) 12 (d) 24
  4. 4.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 66 (c) 110 (d) 55
  5. 5.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  6. 6.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 100 (c) 45 (d) 90
  7. 7.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  8. 8.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 66 (c) 24 (d) 144
  9. 9.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  10. 10.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 132 (c) 24 (d) 66
  11. 11.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 15 (c) 21 (d) 30
  12. 12.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 55 (c) 121 (d) 22
  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) 64 (c) 16 (d) 56
  14. 14.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 91 (c) 156 (d) 169
  15. 15.3 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) 18 (b) 12 (c) 9 (d) 6
  16. 16.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  17. 17.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 25 (d) 10
  18. 18.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 20 (d) 25
  19. 19.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  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) 112 (b) 64 (c) 56 (d) 15
  21. 21.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 120 (d) 105
  22. 22.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) 18 (b) 36 (c) 21 (d) 9
  23. 23.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) 8 (b) 18 (c) 12 (d) 24
  24. 24.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 156 (d) 169
  25. 25.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 45 (d) 90
  26. 26.7 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
  27. 27.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 28 (d) 49
  28. 28.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 36 (d) 81
  29. 29.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 21 (d) 15
  30. 30.8 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) 11 (b) 24 (c) 32 (d) 48
  31. 31.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 14 (c) 21 (d) 28
  32. 32.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  33. 33.3 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) 7 (b) 15 (c) 24 (d) 12
  34. 34.8 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) 48 (b) 14 (c) 96 (d) 56
  35. 35.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
  36. 36.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  37. 37.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 15 (c) 8 (d) 30
  38. 38.7 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) 84 (b) 49 (c) 42 (d) 13
  39. 39.There are 7 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) 98 (b) 49 (c) 14 (d) 56
  40. 40.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 10 (c) 25 (d) 20

Answer key

  1. 55
  2. 28
  3. 12
  4. 55
  5. 6
  6. 45
  7. 120
  8. 66
  9. 6
  10. 132
  11. 15
  12. 110
  13. 56
  14. 78
  15. 9
  16. 24
  17. 10
  18. 20
  19. 24
  20. 56
  21. 105
  22. 18
  23. 12
  24. 78
  25. 90
  26. 35
  27. 21
  28. 36
  29. 15
  30. 24
  31. 14
  32. 120
  33. 12
  34. 48
  35. 36
  36. 24
  37. 15
  38. 42
  39. 49
  40. 10

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