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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 238 · 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. 1.8 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) 14 (b) 48 (c) 96 (d) 56
  2. 2.6 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) 10 (b) 30 (c) 48 (d) 24
  3. 3.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 10 (c) 25 (d) 20
  4. 4.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
  5. 5.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 55 (c) 22 (d) 110
  6. 6.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 15 (d) 12
  7. 7.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  8. 8.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 15 (c) 30 (d) 21
  9. 9.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  10. 10.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 10 (d) 25
  11. 11.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  12. 12.7 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) 98 (c) 14 (d) 56
  13. 13.8 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) 40 (b) 32 (c) 64 (d) 12
  14. 14.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 42 (c) 21 (d) 49
  15. 15.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 105 (d) 210
  16. 16.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 24 (c) 144 (d) 66
  17. 17.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) 48 (b) 56 (c) 14 (d) 96
  18. 18.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) 70 (b) 35 (c) 42 (d) 12
  19. 19.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 14 (c) 42 (d) 21
  20. 20.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  21. 21.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 45 (c) 90 (d) 100
  22. 22.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 110 (d) 55
  23. 23.3 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) 6 (d) 12
  24. 24.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 55 (d) 45
  25. 25.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 56 (c) 36 (d) 28
  26. 26.There are 6 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) 42 (b) 36 (c) 72 (d) 12
  27. 27.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 15 (c) 12 (d) 36
  28. 28.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) 40 (b) 80 (c) 48 (d) 13
  29. 29.4 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) 20 (b) 32 (c) 8 (d) 16
  30. 30.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 28 (c) 42 (d) 21
  31. 31.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 91 (c) 78 (d) 169
  32. 32.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  33. 33.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 56 (d) 16
  34. 34.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 48 (c) 30 (d) 10
  35. 35.4 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) 20 (b) 40 (c) 9 (d) 24
  36. 36.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  37. 37.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 42 (d) 21
  38. 38.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 30 (d) 21
  39. 39.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 55 (c) 121 (d) 110
  40. 40.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 25 (d) 20

Answer key

  1. 48
  2. 24
  3. 10
  4. 6
  5. 110
  6. 15
  7. 120
  8. 15
  9. 120
  10. 10
  11. 120
  12. 49
  13. 32
  14. 21
  15. 105
  16. 132
  17. 48
  18. 35
  19. 21
  20. 120
  21. 90
  22. 55
  23. 6
  24. 45
  25. 28
  26. 36
  27. 30
  28. 40
  29. 16
  30. 21
  31. 78
  32. 120
  33. 28
  34. 24
  35. 20
  36. 24
  37. 42
  38. 15
  39. 55
  40. 10

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