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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 961 · 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. 1.6 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) 9 (b) 18 (c) 36 (d) 24
  2. 2.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 45 (d) 100
  3. 3.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) 32 (b) 20 (c) 16 (d) 8
  4. 4.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 91 (c) 105 (d) 196
  5. 5.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) 11 (b) 35 (c) 30 (d) 60
  6. 6.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 16 (d) 64
  7. 7.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  8. 8.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 81 (c) 72 (d) 45
  9. 9.7 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) 28 (b) 9 (c) 21 (d) 14
  10. 10.6 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) 36 (c) 42 (d) 72
  11. 11.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) 10 (c) 20 (d) 15
  12. 12.7 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) 56 (b) 49 (c) 14 (d) 98
  13. 13.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 45 (c) 100 (d) 90
  14. 14.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 156 (d) 78
  15. 15.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  16. 16.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  17. 17.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 42 (d) 49
  18. 18.3 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) 6 (c) 18 (d) 9
  19. 19.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 105 (d) 91
  20. 20.There are 8 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) 56 (b) 48 (c) 96 (d) 14
  21. 21.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 91 (d) 78
  22. 22.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  23. 23.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 24 (c) 30 (d) 10
  24. 24.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 55 (c) 66 (d) 110
  25. 25.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 25 (c) 10 (d) 21
  26. 26.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 36 (c) 56 (d) 64
  27. 27.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 22 (c) 110 (d) 121
  28. 28.5 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) 15 (b) 30 (c) 20 (d) 8
  29. 29.There are 7 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) 35 (b) 11 (c) 56 (d) 28
  30. 30.3 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) 8 (b) 18 (c) 15 (d) 30
  31. 31.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 90 (c) 55 (d) 100
  32. 32.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 15 (d) 36
  33. 33.6 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) 24 (b) 48 (c) 10 (d) 30
  34. 34.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  35. 35.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  36. 36.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 28 (c) 36 (d) 56
  37. 37.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  38. 38.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 45 (c) 81 (d) 36
  39. 39.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  40. 40.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) 70 (b) 12 (c) 35 (d) 40

Answer key

  1. 18
  2. 45
  3. 16
  4. 91
  5. 30
  6. 56
  7. 120
  8. 36
  9. 14
  10. 36
  11. 10
  12. 49
  13. 45
  14. 78
  15. 24
  16. 6
  17. 21
  18. 9
  19. 91
  20. 48
  21. 78
  22. 120
  23. 24
  24. 55
  25. 20
  26. 28
  27. 55
  28. 15
  29. 28
  30. 15
  31. 45
  32. 15
  33. 24
  34. 6
  35. 120
  36. 28
  37. 120
  38. 36
  39. 6
  40. 35

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