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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 474 · 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.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 45 (d) 81
  2. 2.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 36 (d) 15
  3. 3.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  4. 4.There are 7 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) 21 (b) 9 (c) 28 (d) 14
  5. 5.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 10 (d) 25
  6. 6.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  7. 7.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 12 (d) 9
  8. 8.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  9. 9.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) 8 (b) 30 (c) 15 (d) 18
  10. 10.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 78 (d) 132
  11. 11.There are 3 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) 5 (b) 12 (c) 9 (d) 6
  12. 12.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  13. 13.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 121 (c) 66 (d) 110
  14. 14.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) 56 (b) 96 (c) 14 (d) 48
  15. 15.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
  16. 16.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 121 (d) 55
  17. 17.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  18. 18.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) 10 (b) 42 (c) 24 (d) 21
  19. 19.There are 4 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) 16 (b) 12 (c) 6 (d) 8
  20. 20.There are 6 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) 36 (b) 11 (c) 60 (d) 30
  21. 21.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 49 (d) 21
  22. 22.6 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) 36 (b) 30 (c) 60 (d) 11
  23. 23.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 182 (d) 196
  24. 24.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 144 (c) 78 (d) 132
  25. 25.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 25 (c) 10 (d) 21
  26. 26.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
  27. 27.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 182 (d) 105
  28. 28.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 45 (c) 100 (d) 55
  29. 29.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  30. 30.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  31. 31.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 78 (c) 91 (d) 156
  32. 32.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 18 (d) 36
  33. 33.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 11 (d) 20
  34. 34.7 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) 70 (c) 12 (d) 42
  35. 35.7 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) 56 (b) 28 (c) 35 (d) 11
  36. 36.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 55 (c) 22 (d) 110
  37. 37.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) 12 (d) 40
  38. 38.6 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) 48 (b) 84 (c) 42 (d) 13
  39. 39.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 15 (c) 30 (d) 36
  40. 40.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 240 (d) 20

Answer key

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

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