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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 33 · 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).

NameDateTime takenScore ___ / 40
  1. 1.8 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) 13 (b) 80 (c) 40 (d) 48
  2. 2.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  3. 3.There are 8 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) 64 (b) 56 (c) 15 (d) 112
  4. 4.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
  5. 5.10 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
  6. 6.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
  7. 7.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  8. 8.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) 110 (d) 55
  9. 9.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  10. 10.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 105 (d) 182
  11. 11.5 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
  12. 12.3 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) 30 (b) 18 (c) 15 (d) 8
  13. 13.4 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) 7 (b) 24 (c) 16 (d) 12
  14. 14.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
  15. 15.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 72 (d) 81
  16. 16.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 24 (d) 66
  17. 17.6 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) 42 (c) 36 (d) 72
  18. 18.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) 132 (d) 24
  19. 19.7 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
  20. 20.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 144 (c) 66 (d) 78
  21. 21.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) 9 (b) 20 (c) 40 (d) 25
  22. 22.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 210 (c) 225 (d) 120
  23. 23.7 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) 42 (b) 21 (c) 28 (d) 10
  24. 24.There are 8 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) 11 (b) 48 (c) 24 (d) 32
  25. 25.There are 5 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) 8 (b) 20 (c) 30 (d) 15
  26. 26.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
  27. 27.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
  28. 28.7 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) 42 (b) 35 (c) 70 (d) 12
  29. 29.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  30. 30.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
  31. 31.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  32. 32.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 91 (d) 169
  33. 33.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) 36 (b) 12 (c) 72 (d) 42
  34. 34.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  35. 35.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
  36. 36.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
  37. 37.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  38. 38.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  39. 39.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 36 (d) 81
  40. 40.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

Answer key

  1. 40
  2. 24
  3. 56
  4. 15
  5. 45
  6. 30
  7. 120
  8. 110
  9. 120
  10. 91
  11. 10
  12. 15
  13. 12
  14. 20
  15. 36
  16. 66
  17. 36
  18. 132
  19. 49
  20. 66
  21. 20
  22. 105
  23. 21
  24. 24
  25. 15
  26. 28
  27. 55
  28. 35
  29. 6
  30. 6
  31. 120
  32. 78
  33. 36
  34. 24
  35. 15
  36. 21
  37. 6
  38. 24
  39. 36
  40. 10

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