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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 219 · 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.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
  2. 2.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 36 (d) 30
  3. 3.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  4. 4.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  5. 5.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 8 (c) 20 (d) 15
  6. 6.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 28 (c) 64 (d) 16
  7. 7.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  8. 8.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  9. 9.10 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
  10. 10.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 21 (d) 28
  11. 11.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
  12. 12.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  13. 13.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  14. 14.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 81 (c) 45 (d) 36
  15. 15.3 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) 12 (b) 9 (c) 6 (d) 18
  16. 16.There are 3 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) 24 (b) 21 (c) 10 (d) 42
  17. 17.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55
  18. 18.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) 72 (c) 42 (d) 36
  19. 19.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) 20 (d) 10
  20. 20.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  21. 21.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 45 (c) 20 (d) 100
  22. 22.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 182 (c) 91 (d) 105
  23. 23.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 64 (c) 56 (d) 36
  24. 24.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  25. 25.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 20 (d) 45
  26. 26.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  27. 27.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 30 (d) 15
  28. 28.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
  29. 29.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 21 (d) 28
  30. 30.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  31. 31.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 72 (c) 18 (d) 36
  32. 32.4 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) 32 (b) 56 (c) 11 (d) 28
  33. 33.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  34. 34.7 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) 42 (b) 13 (c) 84 (d) 49
  35. 35.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 55 (d) 121
  36. 36.3 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) 18 (b) 30 (c) 15 (d) 8
  37. 37.There are 8 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) 14 (b) 96 (c) 48 (d) 56
  38. 38.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) 20 (b) 7 (c) 10 (d) 15
  39. 39.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) 64 (c) 32 (d) 12
  40. 40.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 36 (d) 81

Answer key

  1. 15
  2. 30
  3. 24
  4. 120
  5. 15
  6. 56
  7. 120
  8. 6
  9. 45
  10. 21
  11. 6
  12. 6
  13. 120
  14. 36
  15. 9
  16. 21
  17. 55
  18. 36
  19. 20
  20. 120
  21. 90
  22. 91
  23. 28
  24. 120
  25. 45
  26. 24
  27. 15
  28. 20
  29. 21
  30. 24
  31. 72
  32. 28
  33. 24
  34. 42
  35. 110
  36. 15
  37. 48
  38. 10
  39. 32
  40. 36

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