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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 663 · 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. 1.5 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) 12 (b) 70 (c) 35 (d) 40
  2. 2.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) 20 (b) 16 (c) 8 (d) 32
  3. 3.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  4. 4.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 100 (d) 45
  5. 5.There are 4 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) 8 (c) 32 (d) 16
  6. 6.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 56 (d) 28
  7. 7.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 66 (d) 132
  8. 8.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 144 (d) 132
  9. 9.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 28 (c) 42 (d) 21
  10. 10.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  11. 11.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  12. 12.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 25 (d) 20
  13. 13.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 10 (d) 25
  14. 14.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  15. 15.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 45 (c) 90 (d) 100
  16. 16.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 56 (d) 28
  17. 17.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 12 (d) 15
  18. 18.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  19. 19.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) 40 (b) 9 (c) 20 (d) 25
  20. 20.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 21 (c) 15 (d) 36
  21. 21.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 132 (d) 66
  22. 22.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) 30 (c) 15 (d) 8
  23. 23.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 20 (c) 25 (d) 10
  24. 24.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 36 (d) 18
  25. 25.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  26. 26.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  27. 27.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  28. 28.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 45 (c) 90 (d) 55
  29. 29.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
  30. 30.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 81 (d) 72
  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) 9 (b) 6 (c) 5 (d) 12
  32. 32.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 16 (c) 12 (d) 6
  33. 33.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 105 (c) 225 (d) 210
  34. 34.4 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) 8 (b) 6 (c) 16 (d) 12
  35. 35.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) 15 (d) 12
  36. 36.There are 3 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) 18 (b) 12 (c) 9 (d) 6
  37. 37.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 14 (c) 49 (d) 21
  38. 38.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 28 (d) 56
  39. 39.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 32 (c) 64 (d) 40
  40. 40.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 72 (d) 81

Answer key

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

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