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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 282 · 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.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  2. 2.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  3. 3.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  4. 4.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 15 (d) 25
  5. 5.There are 4 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) 12 (b) 6 (c) 16 (d) 8
  6. 6.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  7. 7.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 36 (d) 72
  8. 8.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) 9 (b) 20 (c) 24 (d) 40
  9. 9.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 36 (c) 64 (d) 28
  10. 10.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) 15 (b) 8 (c) 30 (d) 20
  11. 11.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 15 (d) 10
  12. 12.There are 8 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) 32 (c) 16 (d) 10
  13. 13.7 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) 28 (b) 21 (c) 10 (d) 42
  14. 14.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  15. 15.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) 40 (b) 12 (c) 70 (d) 35
  16. 16.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 210 (d) 225
  17. 17.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 21 (d) 28
  18. 18.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 55 (c) 45 (d) 100
  19. 19.There are 8 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) 80 (b) 48 (c) 40 (d) 13
  20. 20.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  21. 21.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 10 (d) 11
  22. 22.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) 10 (d) 20
  23. 23.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 55 (d) 22
  24. 24.7 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) 14 (b) 21 (c) 9 (d) 28
  25. 25.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 81 (c) 36 (d) 72
  26. 26.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) 10 (b) 24 (c) 42 (d) 21
  27. 27.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 66 (d) 144
  28. 28.5 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) 50 (b) 10 (c) 30 (d) 25
  29. 29.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 72 (c) 12 (d) 42
  30. 30.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  31. 31.4 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) 8 (b) 20 (c) 32 (d) 16
  32. 32.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 24 (c) 48 (d) 32
  33. 33.3 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) 24 (b) 21 (c) 42 (d) 10
  34. 34.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) 9 (b) 5 (c) 12 (d) 6
  35. 35.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  36. 36.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 55 (d) 100
  37. 37.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 56 (c) 11 (d) 32
  38. 38.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  39. 39.There are 3 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) 18 (b) 8 (c) 15 (d) 30
  40. 40.6 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) 36 (d) 42

Answer key

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

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