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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 956 · 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.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) 11 (b) 60 (c) 36 (d) 30
  2. 2.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  3. 3.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  4. 4.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 156 (c) 169 (d) 78
  5. 5.6 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) 13 (b) 84 (c) 42 (d) 48
  6. 6.8 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) 24 (b) 16 (c) 32 (d) 10
  7. 7.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 132 (d) 78
  8. 8.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  9. 9.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  10. 10.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
  11. 11.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 78 (c) 91 (d) 156
  12. 12.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 81 (d) 45
  13. 13.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 49 (c) 42 (d) 14
  14. 14.7 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
  15. 15.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 105 (d) 210
  16. 16.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 225 (c) 210 (d) 120
  17. 17.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 30 (d) 15
  18. 18.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 40 (c) 12 (d) 35
  19. 19.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) 15 (b) 64 (c) 56 (d) 112
  20. 20.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 30 (d) 12
  21. 21.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 11 (c) 20 (d) 25
  22. 22.7 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) 56 (b) 35 (c) 11 (d) 28
  23. 23.There are 3 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) 21 (b) 18 (c) 9 (d) 36
  24. 24.8 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) 40 (b) 80 (c) 13 (d) 48
  25. 25.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 100 (c) 45 (d) 55
  26. 26.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 56 (c) 64 (d) 36
  27. 27.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 10 (c) 20 (d) 25
  28. 28.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 45 (c) 90 (d) 100
  29. 29.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  30. 30.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 80 (c) 40 (d) 48
  31. 31.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  32. 32.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 49 (d) 21
  33. 33.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  34. 34.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 20 (d) 25
  35. 35.4 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) 16 (b) 7 (c) 24 (d) 12
  36. 36.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  37. 37.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  38. 38.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 132 (d) 66
  39. 39.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 21 (d) 42
  40. 40.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) 60 (b) 11 (c) 30 (d) 35

Answer key

  1. 30
  2. 6
  3. 24
  4. 78
  5. 42
  6. 16
  7. 66
  8. 120
  9. 6
  10. 15
  11. 78
  12. 36
  13. 42
  14. 21
  15. 105
  16. 105
  17. 30
  18. 35
  19. 56
  20. 15
  21. 10
  22. 28
  23. 18
  24. 40
  25. 45
  26. 28
  27. 10
  28. 90
  29. 24
  30. 40
  31. 24
  32. 21
  33. 6
  34. 10
  35. 12
  36. 120
  37. 120
  38. 132
  39. 21
  40. 30

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