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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 861 · 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 6 players. In how many ways can this be done? (a) 12 (b) 30 (c) 36 (d) 15
  2. 2.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 55 (d) 121
  3. 3.6 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) 18 (b) 24 (c) 12 (d) 8
  4. 4.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 30 (d) 15
  5. 5.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) 13 (c) 48 (d) 40
  6. 6.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 132 (c) 144 (d) 78
  7. 7.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 11 (d) 10
  8. 8.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
  9. 9.7 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) 28 (b) 21 (c) 10 (d) 42
  10. 10.3 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) 9 (b) 36 (c) 18 (d) 21
  11. 11.14 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
  12. 12.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 21 (d) 30
  13. 13.There are 3 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) 18 (b) 36 (c) 21 (d) 9
  14. 14.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  15. 15.There are 7 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) 10 (b) 21 (c) 42 (d) 28
  16. 16.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) 24 (b) 8 (c) 12 (d) 18
  17. 17.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  18. 18.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 132 (d) 24
  19. 19.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) 12 (c) 40 (d) 70
  20. 20.6 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) 13 (b) 42 (c) 84 (d) 48
  21. 21.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 55 (d) 121
  22. 22.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
  23. 23.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  24. 24.7 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) 56 (b) 98 (c) 14 (d) 49
  25. 25.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 225 (d) 210
  26. 26.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) 36 (b) 9 (c) 18 (d) 21
  27. 27.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  28. 28.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 72 (b) 12 (c) 42 (d) 36
  29. 29.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) 56 (c) 112 (d) 15
  30. 30.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  31. 31.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 49 (d) 21
  32. 32.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 28 (d) 16
  33. 33.There are 7 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) 12 (b) 70 (c) 42 (d) 35
  34. 34.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 16 (c) 24 (d) 10
  35. 35.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  36. 36.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) 30 (c) 35 (d) 11
  37. 37.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) 21 (b) 42 (c) 10 (d) 24
  38. 38.3 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) 5 (b) 9 (c) 12 (d) 6
  39. 39.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) 72 (d) 36
  40. 40.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) 90 (d) 45

Answer key

  1. 30
  2. 55
  3. 12
  4. 15
  5. 40
  6. 66
  7. 10
  8. 36
  9. 21
  10. 18
  11. 91
  12. 15
  13. 18
  14. 120
  15. 21
  16. 12
  17. 120
  18. 66
  19. 35
  20. 42
  21. 110
  22. 55
  23. 120
  24. 49
  25. 105
  26. 18
  27. 6
  28. 36
  29. 56
  30. 120
  31. 21
  32. 28
  33. 35
  34. 16
  35. 24
  36. 30
  37. 21
  38. 6
  39. 72
  40. 90

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