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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 893 · 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 captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 14 (c) 42 (d) 49
  2. 2.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 144 (d) 132
  3. 3.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 6 (d) 3
  4. 4.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) 20 (b) 25 (c) 9 (d) 40
  5. 5.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  6. 6.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 11 (c) 35 (d) 56
  7. 7.6 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) 18 (c) 8 (d) 12
  8. 8.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
  9. 9.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 22 (c) 55 (d) 110
  10. 10.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 72 (c) 18 (d) 81
  11. 11.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  12. 12.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  13. 13.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) 49 (b) 13 (c) 42 (d) 84
  14. 14.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  15. 15.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  16. 16.There are 4 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) 40 (b) 9 (c) 20 (d) 24
  17. 17.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  18. 18.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 16 (d) 28
  19. 19.7 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
  20. 20.There are 4 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) 48 (b) 10 (c) 28 (d) 24
  21. 21.There are 3 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) 7 (b) 24 (c) 15 (d) 12
  22. 22.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 25 (b) 40 (c) 9 (d) 20
  23. 23.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  24. 24.4 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) 40 (d) 20
  25. 25.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 91 (c) 105 (d) 196
  26. 26.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 120 (c) 105 (d) 210
  27. 27.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 18 (d) 36
  28. 28.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
  29. 29.3 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) 15 (b) 12 (c) 7 (d) 24
  30. 30.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 15 (d) 30
  31. 31.3 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) 18 (c) 9 (d) 6
  32. 32.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 105 (d) 120
  33. 33.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 45 (c) 90 (d) 20
  34. 34.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55
  35. 35.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
  36. 36.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 15 (c) 25 (d) 10
  37. 37.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) 42 (b) 12 (c) 36 (d) 72
  38. 38.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  39. 39.4 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) 16 (b) 8 (c) 12 (d) 6
  40. 40.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 15 (d) 30

Answer key

  1. 42
  2. 66
  3. 6
  4. 20
  5. 120
  6. 28
  7. 12
  8. 10
  9. 110
  10. 72
  11. 120
  12. 24
  13. 42
  14. 24
  15. 24
  16. 20
  17. 6
  18. 28
  19. 21
  20. 24
  21. 12
  22. 20
  23. 120
  24. 20
  25. 91
  26. 105
  27. 36
  28. 36
  29. 12
  30. 15
  31. 9
  32. 105
  33. 45
  34. 55
  35. 55
  36. 10
  37. 36
  38. 120
  39. 8
  40. 15

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