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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 166 · 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.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) 18 (b) 24 (c) 36 (d) 9
  2. 2.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 105 (c) 182 (d) 196
  3. 3.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 66 (d) 144
  4. 4.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  5. 5.8 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) 48 (b) 14 (c) 56 (d) 96
  6. 6.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  7. 7.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 90 (d) 45
  8. 8.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 210 (c) 105 (d) 120
  9. 9.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) 36 (d) 18
  10. 10.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 30 (c) 15 (d) 8
  11. 11.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  12. 12.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 91 (d) 105
  13. 13.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 6 (c) 12 (d) 9
  14. 14.There are 4 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) 16 (b) 7 (c) 24 (d) 12
  15. 15.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 144 (c) 24 (d) 132
  16. 16.There are 5 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) 40 (b) 12 (c) 35 (d) 70
  17. 17.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  18. 18.There are 5 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) 7 (b) 15 (c) 10 (d) 20
  19. 19.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 10 (d) 20
  20. 20.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  21. 21.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 42 (c) 28 (d) 49
  22. 22.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 42 (c) 49 (d) 14
  23. 23.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  24. 24.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 30 (d) 12
  25. 25.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 55 (d) 100
  26. 26.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 21 (c) 28 (d) 42
  27. 27.6 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) 12 (b) 72 (c) 42 (d) 36
  28. 28.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
  29. 29.7 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) 35 (b) 70 (c) 12 (d) 42
  30. 30.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  31. 31.3 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) 12 (b) 9 (c) 5 (d) 6
  32. 32.4 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) 32 (b) 20 (c) 16 (d) 8
  33. 33.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 10 (c) 11 (d) 25
  34. 34.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 16 (c) 64 (d) 28
  35. 35.10 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
  36. 36.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) 15 (b) 10 (c) 7 (d) 20
  37. 37.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 32 (c) 16 (d) 20
  38. 38.There are 5 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) 10 (b) 25 (c) 30 (d) 50
  39. 39.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  40. 40.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) 8 (b) 30 (c) 15 (d) 20

Answer key

  1. 18
  2. 91
  3. 66
  4. 120
  5. 48
  6. 120
  7. 90
  8. 105
  9. 72
  10. 15
  11. 6
  12. 91
  13. 9
  14. 12
  15. 132
  16. 35
  17. 24
  18. 10
  19. 10
  20. 120
  21. 21
  22. 42
  23. 6
  24. 30
  25. 45
  26. 21
  27. 36
  28. 15
  29. 35
  30. 24
  31. 6
  32. 16
  33. 10
  34. 56
  35. 45
  36. 10
  37. 16
  38. 25
  39. 24
  40. 15

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