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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 776 · 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. 1.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 78 (c) 169 (d) 156
  2. 2.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 64 (c) 56 (d) 112
  3. 3.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  4. 4.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 16 (c) 64 (d) 28
  5. 5.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 20 (d) 10
  6. 6.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) 60 (b) 11 (c) 36 (d) 30
  7. 7.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 21 (d) 42
  8. 8.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  9. 9.3 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) 6 (b) 12 (c) 18 (d) 9
  10. 10.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  11. 11.There are 4 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) 6 (c) 12 (d) 16
  12. 12.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  13. 13.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
  14. 14.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  15. 15.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 144 (d) 66
  16. 16.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) 14 (b) 56 (c) 96 (d) 48
  17. 17.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  18. 18.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 121 (c) 66 (d) 110
  19. 19.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 10 (d) 20
  20. 20.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 72 (d) 81
  21. 21.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 210 (d) 225
  22. 22.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 30 (d) 12
  23. 23.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) 28 (b) 24 (c) 48 (d) 10
  24. 24.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 36 (c) 64 (d) 56
  25. 25.4 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) 8 (b) 12 (c) 16 (d) 6
  26. 26.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  27. 27.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) 12 (b) 72 (c) 36 (d) 42
  28. 28.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) 28 (c) 11 (d) 56
  29. 29.There are 3 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) 12 (b) 6 (c) 9 (d) 18
  30. 30.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 132 (c) 78 (d) 66
  31. 31.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) 24 (b) 10 (c) 42 (d) 21
  32. 32.5 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
  33. 33.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 56 (d) 28
  34. 34.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 225 (c) 120 (d) 105
  35. 35.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 105 (c) 91 (d) 182
  36. 36.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 81 (d) 36
  37. 37.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) 25 (c) 20 (d) 40
  38. 38.There are 7 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) 98 (b) 14 (c) 56 (d) 49
  39. 39.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 132 (d) 144
  40. 40.There are 4 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) 10 (b) 48 (c) 24 (d) 28

Answer key

  1. 78
  2. 56
  3. 120
  4. 56
  5. 20
  6. 30
  7. 21
  8. 6
  9. 9
  10. 6
  11. 8
  12. 120
  13. 45
  14. 24
  15. 66
  16. 48
  17. 24
  18. 55
  19. 10
  20. 36
  21. 105
  22. 30
  23. 24
  24. 28
  25. 8
  26. 24
  27. 36
  28. 28
  29. 9
  30. 66
  31. 21
  32. 10
  33. 28
  34. 105
  35. 91
  36. 36
  37. 20
  38. 49
  39. 132
  40. 24

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