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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 187 · 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 11 players. In how many ways can this be done? (a) 121 (b) 22 (c) 110 (d) 55
  2. 2.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 14 (d) 42
  3. 3.4 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) 8 (b) 16 (c) 32 (d) 20
  4. 4.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  5. 5.7 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) 42 (b) 28 (c) 21 (d) 10
  6. 6.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) 36 (b) 72 (c) 12 (d) 42
  7. 7.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 72 (c) 18 (d) 81
  8. 8.5 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) 60 (b) 30 (c) 35 (d) 11
  9. 9.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 8 (c) 32 (d) 16
  10. 10.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  11. 11.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  12. 12.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 66 (c) 24 (d) 132
  13. 13.7 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) 70 (b) 12 (c) 42 (d) 35
  14. 14.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 49 (d) 28
  15. 15.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) 12 (b) 9 (c) 5 (d) 6
  16. 16.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
  17. 17.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  18. 18.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 21 (d) 49
  19. 19.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 42 (d) 21
  20. 20.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 144 (d) 132
  21. 21.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 36 (d) 15
  22. 22.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 132 (d) 144
  23. 23.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 10 (d) 20
  24. 24.7 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) 11 (b) 35 (c) 28 (d) 56
  25. 25.15 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
  26. 26.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 156 (c) 78 (d) 91
  27. 27.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) 48 (c) 80 (d) 13
  28. 28.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) 10 (b) 20 (c) 7 (d) 15
  29. 29.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  30. 30.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 156 (c) 169 (d) 78
  31. 31.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 21 (c) 30 (d) 36
  32. 32.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 20 (c) 15 (d) 7
  33. 33.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  34. 34.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 16 (c) 28 (d) 56
  35. 35.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) 9 (d) 24
  36. 36.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) 30 (c) 60 (d) 11
  37. 37.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) 18 (b) 9 (c) 6 (d) 12
  38. 38.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  39. 39.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 110 (c) 121 (d) 66
  40. 40.There are 4 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) 11 (b) 28 (c) 56 (d) 32

Answer key

  1. 110
  2. 42
  3. 16
  4. 24
  5. 21
  6. 36
  7. 36
  8. 30
  9. 16
  10. 120
  11. 24
  12. 132
  13. 35
  14. 21
  15. 6
  16. 20
  17. 6
  18. 21
  19. 21
  20. 66
  21. 15
  22. 66
  23. 10
  24. 28
  25. 105
  26. 78
  27. 40
  28. 10
  29. 6
  30. 78
  31. 15
  32. 10
  33. 120
  34. 56
  35. 20
  36. 30
  37. 9
  38. 120
  39. 55
  40. 28

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