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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 385 · 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. 1.6 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) 8 (b) 24 (c) 12 (d) 18
  2. 2.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 45 (d) 90
  3. 3.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 14 (d) 42
  4. 4.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 121 (d) 55
  5. 5.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 91 (d) 105
  6. 6.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 182 (c) 105 (d) 91
  7. 7.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 10 (c) 25 (d) 11
  8. 8.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  9. 9.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
  10. 10.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 91 (c) 156 (d) 169
  11. 11.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 132 (c) 24 (d) 144
  12. 12.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  13. 13.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) 18 (c) 15 (d) 30
  14. 14.There are 6 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) 18 (b) 36 (c) 24 (d) 9
  15. 15.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 72 (d) 36
  16. 16.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
  17. 17.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) 40 (b) 12 (c) 64 (d) 32
  18. 18.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  19. 19.4 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) 10 (c) 28 (d) 24
  20. 20.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  21. 21.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 12 (d) 15
  22. 22.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) 12 (c) 24 (d) 7
  23. 23.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  24. 24.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 36 (c) 81 (d) 72
  25. 25.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  26. 26.There are 5 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) 15 (b) 20 (c) 10 (d) 7
  27. 27.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 132 (d) 24
  28. 28.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
  29. 29.7 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) 49 (b) 56 (c) 98 (d) 14
  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) 80 (b) 40 (c) 48 (d) 13
  31. 31.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  32. 32.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 64 (c) 28 (d) 36
  33. 33.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  34. 34.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 10 (c) 21 (d) 20
  35. 35.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 100 (d) 45
  36. 36.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) 10 (c) 24 (d) 16
  37. 37.11 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
  38. 38.5 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
  39. 39.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 55 (d) 121
  40. 40.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 36 (c) 81 (d) 72

Answer key

  1. 12
  2. 45
  3. 21
  4. 55
  5. 91
  6. 91
  7. 10
  8. 6
  9. 15
  10. 78
  11. 132
  12. 120
  13. 15
  14. 18
  15. 36
  16. 28
  17. 32
  18. 24
  19. 24
  20. 6
  21. 15
  22. 12
  23. 120
  24. 36
  25. 24
  26. 10
  27. 66
  28. 56
  29. 49
  30. 40
  31. 24
  32. 28
  33. 120
  34. 20
  35. 45
  36. 16
  37. 55
  38. 10
  39. 55
  40. 72

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