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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 637 · 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).

NameDateTime takenScore ___ / 40
  1. 1.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 81 (c) 36 (d) 72
  2. 2.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) 12 (b) 42 (c) 36 (d) 72
  3. 3.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  4. 4.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 55 (c) 66 (d) 110
  5. 5.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 169 (c) 91 (d) 156
  6. 6.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 36 (c) 24 (d) 18
  7. 7.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 11 (c) 35 (d) 60
  8. 8.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 45 (c) 20 (d) 90
  9. 9.There are 3 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) 8 (b) 15 (c) 30 (d) 18
  10. 10.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) 9 (d) 12
  11. 11.4 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) 24 (b) 9 (c) 20 (d) 40
  12. 12.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 55 (c) 22 (d) 121
  13. 13.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 14 (c) 49 (d) 42
  14. 14.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 121 (c) 110 (d) 22
  15. 15.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) 66 (d) 144
  16. 16.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  17. 17.7 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) 98 (b) 14 (c) 56 (d) 49
  18. 18.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  19. 19.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 49 (c) 42 (d) 28
  20. 20.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 225 (d) 120
  21. 21.There are 6 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) 24 (b) 8 (c) 18 (d) 12
  22. 22.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 105 (c) 91 (d) 196
  23. 23.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  24. 24.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  25. 25.4 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) 7 (b) 24 (c) 16 (d) 12
  26. 26.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  27. 27.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  28. 28.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
  29. 29.There are 6 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) 48 (b) 10 (c) 30 (d) 24
  30. 30.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  31. 31.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  32. 32.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 10 (c) 25 (d) 15
  33. 33.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
  34. 34.3 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) 30 (b) 15 (c) 8 (d) 18
  35. 35.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 25 (c) 10 (d) 20
  36. 36.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  37. 37.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 30 (d) 15
  38. 38.There are 7 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) 49 (b) 56 (c) 98 (d) 14
  39. 39.5 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) 30 (b) 15 (c) 20 (d) 8
  40. 40.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 56 (d) 28

Answer key

  1. 36
  2. 36
  3. 24
  4. 55
  5. 78
  6. 18
  7. 30
  8. 45
  9. 15
  10. 9
  11. 20
  12. 55
  13. 21
  14. 110
  15. 132
  16. 120
  17. 49
  18. 24
  19. 21
  20. 105
  21. 12
  22. 91
  23. 24
  24. 120
  25. 12
  26. 24
  27. 120
  28. 10
  29. 24
  30. 6
  31. 6
  32. 10
  33. 45
  34. 15
  35. 20
  36. 120
  37. 15
  38. 49
  39. 15
  40. 28

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