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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 8 · 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. 1.8 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) 32 (b) 11 (c) 24 (d) 48
  2. 2.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 66 (d) 132
  3. 3.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  4. 4.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
  5. 5.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 24 (d) 144
  6. 6.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 16 (c) 32 (d) 24
  7. 7.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  8. 8.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) 18 (b) 9 (c) 21 (d) 36
  9. 9.5 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) 40 (b) 9 (c) 25 (d) 20
  10. 10.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  11. 11.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 28 (d) 16
  12. 12.5 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
  13. 13.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 169 (c) 91 (d) 156
  14. 14.8 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) 64 (b) 112 (c) 56 (d) 15
  15. 15.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 40 (c) 24 (d) 9
  16. 16.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 25 (d) 10
  17. 17.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 36 (d) 15
  18. 18.10 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
  19. 19.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 36 (c) 81 (d) 72
  20. 20.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 25 (d) 15
  21. 21.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) 72 (b) 12 (c) 42 (d) 36
  22. 22.7 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
  23. 23.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  24. 24.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) 35 (b) 11 (c) 28 (d) 56
  25. 25.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 28 (c) 24 (d) 48
  26. 26.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
  27. 27.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
  28. 28.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
  29. 29.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 21 (c) 49 (d) 42
  30. 30.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  31. 31.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 18 (c) 36 (d) 9
  32. 32.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
  33. 33.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 64 (c) 56 (d) 28
  34. 34.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  35. 35.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) 35 (b) 11 (c) 30 (d) 60
  36. 36.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) 14 (d) 49
  37. 37.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
  38. 38.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 36 (c) 21 (d) 30
  39. 39.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  40. 40.There are 6 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) 8 (b) 12 (c) 24 (d) 18

Answer key

  1. 24
  2. 66
  3. 24
  4. 90
  5. 66
  6. 16
  7. 24
  8. 18
  9. 20
  10. 6
  11. 56
  12. 35
  13. 78
  14. 56
  15. 20
  16. 10
  17. 15
  18. 45
  19. 72
  20. 10
  21. 36
  22. 21
  23. 120
  24. 28
  25. 24
  26. 45
  27. 30
  28. 10
  29. 21
  30. 6
  31. 18
  32. 105
  33. 28
  34. 24
  35. 30
  36. 42
  37. 132
  38. 15
  39. 120
  40. 12

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