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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 111 · 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. 1.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 21 (d) 49
  2. 2.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 66 (d) 24
  3. 3.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 81 (c) 36 (d) 45
  4. 4.3 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) 12 (b) 24 (c) 15 (d) 7
  5. 5.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  6. 6.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 96 (b) 56 (c) 48 (d) 14
  7. 7.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  8. 8.There are 8 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) 48 (b) 13 (c) 40 (d) 80
  9. 9.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  10. 10.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  11. 11.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 10 (c) 25 (d) 21
  12. 12.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 55 (c) 121 (d) 22
  13. 13.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 45 (c) 81 (d) 72
  14. 14.15 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
  15. 15.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 30 (d) 15
  16. 16.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  17. 17.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 91 (d) 182
  18. 18.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 132 (d) 66
  19. 19.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) 84 (b) 42 (c) 48 (d) 13
  20. 20.6 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) 84 (b) 13 (c) 48 (d) 42
  21. 21.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) 42 (d) 72
  22. 22.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 10 (c) 24 (d) 21
  23. 23.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 10 (c) 20 (d) 25
  24. 24.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 13 (c) 48 (d) 80
  25. 25.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 78 (c) 144 (d) 132
  26. 26.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
  27. 27.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 182 (c) 196 (d) 91
  28. 28.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 49 (d) 21
  29. 29.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 28 (c) 64 (d) 36
  30. 30.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  31. 31.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  32. 32.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  33. 33.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 120 (d) 225
  34. 34.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 25 (d) 10
  35. 35.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  36. 36.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) 9 (d) 21
  37. 37.6 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) 60 (b) 36 (c) 30 (d) 11
  38. 38.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 22 (c) 121 (d) 110
  39. 39.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  40. 40.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 8 (c) 18 (d) 12

Answer key

  1. 21
  2. 132
  3. 36
  4. 12
  5. 24
  6. 48
  7. 24
  8. 40
  9. 24
  10. 120
  11. 20
  12. 110
  13. 36
  14. 105
  15. 30
  16. 6
  17. 91
  18. 66
  19. 42
  20. 42
  21. 36
  22. 21
  23. 10
  24. 40
  25. 66
  26. 15
  27. 91
  28. 21
  29. 28
  30. 120
  31. 120
  32. 24
  33. 105
  34. 10
  35. 24
  36. 18
  37. 30
  38. 55
  39. 120
  40. 12

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