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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 172 · 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. 1.11 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
  2. 2.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 10 (c) 21 (d) 42
  3. 3.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 10 (c) 21 (d) 42
  4. 4.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
  5. 5.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) 30 (b) 24 (c) 10 (d) 48
  6. 6.There are 8 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) 48 (b) 11 (c) 32 (d) 24
  7. 7.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 66 (c) 144 (d) 78
  8. 8.There are 7 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) 84 (b) 49 (c) 13 (d) 42
  9. 9.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 49 (d) 21
  10. 10.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  11. 11.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 36 (d) 72
  12. 12.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 20 (c) 10 (d) 25
  13. 13.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  14. 14.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 100 (c) 45 (d) 90
  15. 15.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 49 (d) 21
  16. 16.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 110 (c) 121 (d) 22
  17. 17.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  18. 18.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  19. 19.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 81 (c) 18 (d) 72
  20. 20.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 90 (d) 100
  21. 21.7 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) 21 (b) 10 (c) 28 (d) 42
  22. 22.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 66 (d) 132
  23. 23.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) 12 (d) 18
  24. 24.There are 7 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) 56 (b) 35 (c) 11 (d) 28
  25. 25.8 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) 13 (b) 48 (c) 80 (d) 40
  26. 26.3 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) 24 (b) 7 (c) 12 (d) 15
  27. 27.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 42 (c) 49 (d) 21
  28. 28.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  29. 29.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 5 (c) 12 (d) 9
  30. 30.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 110 (c) 22 (d) 121
  31. 31.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 15 (c) 36 (d) 30
  32. 32.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  33. 33.There are 8 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) 112 (b) 15 (c) 56 (d) 64
  34. 34.There are 5 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) 25 (b) 40 (c) 9 (d) 20
  35. 35.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  36. 36.4 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) 28 (b) 56 (c) 32 (d) 11
  37. 37.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 10 (c) 25 (d) 20
  38. 38.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 12 (d) 15
  39. 39.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 42 (c) 84 (d) 49
  40. 40.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 90 (d) 100

Answer key

  1. 55
  2. 21
  3. 21
  4. 36
  5. 24
  6. 24
  7. 66
  8. 42
  9. 21
  10. 24
  11. 36
  12. 20
  13. 6
  14. 45
  15. 21
  16. 55
  17. 120
  18. 120
  19. 36
  20. 90
  21. 21
  22. 66
  23. 12
  24. 28
  25. 40
  26. 12
  27. 42
  28. 24
  29. 6
  30. 110
  31. 15
  32. 6
  33. 56
  34. 20
  35. 120
  36. 28
  37. 10
  38. 30
  39. 42
  40. 45

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