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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 673 · 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 10 players. In how many ways can this be done? (a) 20 (b) 90 (c) 100 (d) 45
  2. 2.There are 4 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) 40 (b) 20 (c) 24 (d) 9
  3. 3.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 12 (d) 30
  4. 4.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 45 (c) 55 (d) 90
  5. 5.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 55 (d) 66
  6. 6.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 81 (d) 72
  7. 7.7 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) 14 (c) 98 (d) 49
  8. 8.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  9. 9.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
  10. 10.12 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
  11. 11.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) 6 (b) 9 (c) 5 (d) 12
  12. 12.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 11 (d) 20
  13. 13.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 20 (d) 10
  14. 14.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) 12 (b) 32 (c) 64 (d) 40
  15. 15.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 182 (c) 105 (d) 196
  16. 16.There are 5 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) 50 (b) 30 (c) 25 (d) 10
  17. 17.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  18. 18.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  19. 19.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 110 (d) 55
  20. 20.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 78 (c) 66 (d) 144
  21. 21.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 36 (c) 15 (d) 21
  22. 22.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 84 (c) 42 (d) 48
  23. 23.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  24. 24.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 12 (c) 9 (d) 18
  25. 25.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 16 (d) 56
  26. 26.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 42 (d) 21
  27. 27.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) 18 (b) 8 (c) 24 (d) 12
  28. 28.6 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) 24 (b) 18 (c) 36 (d) 9
  29. 29.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 36 (d) 18
  30. 30.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 96 (b) 14 (c) 48 (d) 56
  31. 31.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  32. 32.4 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) 32 (b) 8 (c) 20 (d) 16
  33. 33.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) 20 (b) 8 (c) 30 (d) 15
  34. 34.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 78 (c) 156 (d) 169
  35. 35.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 182 (d) 196
  36. 36.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
  37. 37.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  38. 38.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 42 (d) 49
  39. 39.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  40. 40.11 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

Answer key

  1. 90
  2. 20
  3. 15
  4. 45
  5. 55
  6. 72
  7. 49
  8. 120
  9. 78
  10. 66
  11. 6
  12. 10
  13. 20
  14. 32
  15. 91
  16. 25
  17. 6
  18. 120
  19. 110
  20. 66
  21. 15
  22. 42
  23. 24
  24. 9
  25. 28
  26. 21
  27. 12
  28. 18
  29. 36
  30. 48
  31. 6
  32. 16
  33. 15
  34. 78
  35. 91
  36. 132
  37. 120
  38. 21
  39. 24
  40. 55

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