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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 122 · 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 how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  2. 2.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
  3. 3.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 105 (c) 120 (d) 225
  4. 4.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 100 (c) 55 (d) 45
  5. 5.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 144 (c) 132 (d) 66
  6. 6.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
  7. 7.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) 21 (d) 42
  8. 8.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 66 (c) 110 (d) 121
  9. 9.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  10. 10.3 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) 9 (b) 6 (c) 12 (d) 18
  11. 11.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  12. 12.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 15 (d) 36
  13. 13.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  14. 14.There are 6 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) 84 (b) 42 (c) 48 (d) 13
  15. 15.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 40 (c) 20 (d) 9
  16. 16.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  17. 17.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 21 (d) 30
  18. 18.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  19. 19.6 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) 9 (d) 36
  20. 20.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 66 (c) 24 (d) 144
  21. 21.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 20 (d) 11
  22. 22.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 78 (d) 66
  23. 23.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 49 (c) 42 (d) 21
  24. 24.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  25. 25.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 15 (d) 20
  26. 26.4 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) 16 (b) 12 (c) 6 (d) 8
  27. 27.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 121 (c) 55 (d) 22
  28. 28.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
  29. 29.5 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) 70 (b) 35 (c) 40 (d) 12
  30. 30.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) 30 (c) 15 (d) 8
  31. 31.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 42 (d) 14
  32. 32.7 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) 10 (c) 28 (d) 21
  33. 33.There are 3 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) 6 (c) 12 (d) 9
  34. 34.7 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) 21 (b) 9 (c) 14 (d) 28
  35. 35.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  36. 36.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 105 (d) 182
  37. 37.6 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) 84 (b) 42 (c) 13 (d) 48
  38. 38.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) 9 (b) 21 (c) 28 (d) 14
  39. 39.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 91 (c) 78 (d) 169
  40. 40.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

Answer key

  1. 6
  2. 21
  3. 105
  4. 45
  5. 66
  6. 48
  7. 42
  8. 55
  9. 120
  10. 9
  11. 120
  12. 15
  13. 120
  14. 42
  15. 20
  16. 24
  17. 15
  18. 120
  19. 18
  20. 132
  21. 10
  22. 66
  23. 21
  24. 6
  25. 10
  26. 8
  27. 55
  28. 72
  29. 35
  30. 15
  31. 21
  32. 21
  33. 9
  34. 14
  35. 120
  36. 91
  37. 42
  38. 14
  39. 78
  40. 20

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