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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 488 · 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 a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 55 (c) 121 (d) 66
  2. 2.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 45 (c) 90 (d) 100
  3. 3.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  4. 4.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) 18 (b) 36 (c) 21 (d) 9
  5. 5.6 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) 36 (b) 9 (c) 18 (d) 24
  6. 6.11 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
  7. 7.3 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) 18 (b) 30 (c) 15 (d) 8
  8. 8.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 28 (d) 49
  9. 9.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 78 (d) 91
  10. 10.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 100 (c) 45 (d) 55
  11. 11.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  12. 12.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 28 (d) 16
  13. 13.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 81 (c) 18 (d) 72
  14. 14.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  15. 15.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  16. 16.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 20 (c) 10 (d) 21
  17. 17.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 49 (c) 21 (d) 14
  18. 18.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 55 (d) 121
  19. 19.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  20. 20.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  21. 21.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 6 (d) 3
  22. 22.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 30 (c) 36 (d) 60
  23. 23.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
  24. 24.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 36 (c) 18 (d) 81
  25. 25.6 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) 24 (b) 8 (c) 18 (d) 12
  26. 26.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
  27. 27.7 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) 70 (b) 42 (c) 12 (d) 35
  28. 28.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 10 (c) 15 (d) 20
  29. 29.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 210 (d) 105
  30. 30.There are 3 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) 24 (b) 12 (c) 7 (d) 15
  31. 31.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 21 (d) 49
  32. 32.5 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) 10 (b) 7 (c) 15 (d) 20
  33. 33.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 84 (c) 42 (d) 48
  34. 34.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 10 (d) 20
  35. 35.4 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) 16 (b) 32 (c) 20 (d) 8
  36. 36.There are 6 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) 42 (b) 84 (c) 13 (d) 48
  37. 37.8 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) 24 (c) 48 (d) 11
  38. 38.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 36 (c) 21 (d) 15
  39. 39.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 182 (c) 91 (d) 196
  40. 40.5 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) 60 (b) 11 (c) 35 (d) 30

Answer key

  1. 55
  2. 45
  3. 120
  4. 18
  5. 18
  6. 55
  7. 15
  8. 21
  9. 78
  10. 45
  11. 24
  12. 28
  13. 36
  14. 120
  15. 6
  16. 20
  17. 42
  18. 110
  19. 24
  20. 120
  21. 6
  22. 30
  23. 66
  24. 72
  25. 12
  26. 78
  27. 35
  28. 10
  29. 105
  30. 12
  31. 21
  32. 10
  33. 42
  34. 10
  35. 16
  36. 42
  37. 24
  38. 15
  39. 91
  40. 30

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