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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 733 · 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. 1.7 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) 28 (b) 14 (c) 21 (d) 9
  2. 2.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) 16 (b) 12 (c) 24 (d) 7
  3. 3.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) 8 (b) 32 (c) 16 (d) 20
  4. 4.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 28 (d) 64
  5. 5.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 21 (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) 55 (b) 110 (c) 121 (d) 22
  7. 7.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
  8. 8.4 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) 16 (b) 8 (c) 20 (d) 32
  9. 9.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 120 (c) 210 (d) 105
  10. 10.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 30 (c) 60 (d) 11
  11. 11.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 36 (c) 28 (d) 64
  12. 12.12 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
  13. 13.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  14. 14.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 55 (d) 121
  15. 15.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  16. 16.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 84 (c) 42 (d) 49
  17. 17.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 20 (c) 100 (d) 45
  18. 18.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 132 (d) 144
  19. 19.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  20. 20.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  21. 21.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 49 (d) 28
  22. 22.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 20 (d) 25
  23. 23.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  24. 24.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 28 (c) 49 (d) 42
  25. 25.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) 12 (c) 8 (d) 16
  26. 26.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 35 (c) 11 (d) 30
  27. 27.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) 42 (b) 10 (c) 24 (d) 21
  28. 28.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 100 (c) 90 (d) 20
  29. 29.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 144 (c) 132 (d) 24
  30. 30.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) 40 (c) 80 (d) 13
  31. 31.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) 12 (b) 70 (c) 40 (d) 35
  32. 32.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 110 (c) 55 (d) 66
  33. 33.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 10 (d) 20
  34. 34.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10
  35. 35.There are 5 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) 15 (b) 30 (c) 8 (d) 20
  36. 36.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  37. 37.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
  38. 38.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) 28 (b) 56 (c) 32 (d) 11
  39. 39.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 30 (d) 12
  40. 40.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 156 (c) 91 (d) 78

Answer key

  1. 14
  2. 12
  3. 16
  4. 28
  5. 20
  6. 110
  7. 72
  8. 16
  9. 105
  10. 30
  11. 28
  12. 66
  13. 6
  14. 55
  15. 120
  16. 42
  17. 90
  18. 66
  19. 24
  20. 24
  21. 21
  22. 10
  23. 120
  24. 21
  25. 8
  26. 30
  27. 21
  28. 45
  29. 132
  30. 40
  31. 35
  32. 55
  33. 10
  34. 10
  35. 15
  36. 24
  37. 45
  38. 28
  39. 30
  40. 78

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