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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 24 · 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, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 156 (d) 78
  2. 2.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 7 (c) 16 (d) 12
  3. 3.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 36 (c) 64 (d) 28
  4. 4.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 14 (c) 21 (d) 42
  5. 5.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) 24 (b) 11 (c) 48 (d) 32
  6. 6.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  7. 7.3 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) 24 (b) 12 (c) 7 (d) 15
  8. 8.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  9. 9.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  10. 10.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  11. 11.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 64 (c) 28 (d) 36
  12. 12.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  13. 13.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  14. 14.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) 14 (b) 56 (c) 49 (d) 98
  15. 15.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 121 (d) 55
  16. 16.3 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) 9 (b) 6 (c) 12 (d) 5
  17. 17.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 72 (d) 36
  18. 18.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) 12 (d) 30
  19. 19.There are 4 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) 20 (b) 9 (c) 24 (d) 40
  20. 20.3 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) 18 (c) 12 (d) 9
  21. 21.5 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) 30 (b) 11 (c) 35 (d) 60
  22. 22.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 36 (d) 15
  23. 23.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) 7 (b) 15 (c) 12 (d) 24
  24. 24.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  25. 25.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 72 (d) 36
  26. 26.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 210 (d) 225
  27. 27.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 5 (b) 6 (c) 9 (d) 12
  28. 28.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 36 (d) 15
  29. 29.7 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) 11 (b) 56 (c) 28 (d) 35
  30. 30.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 210 (c) 120 (d) 225
  31. 31.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 78 (c) 144 (d) 66
  32. 32.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) 22 (d) 121
  33. 33.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) 28 (b) 48 (c) 24 (d) 10
  34. 34.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 21 (d) 42
  35. 35.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
  36. 36.There are 5 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) 25 (b) 40 (c) 9 (d) 20
  37. 37.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  38. 38.8 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) 56 (b) 48 (c) 96 (d) 14
  39. 39.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 182 (c) 91 (d) 196
  40. 40.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 30 (c) 18 (d) 8

Answer key

  1. 78
  2. 12
  3. 28
  4. 21
  5. 24
  6. 6
  7. 12
  8. 6
  9. 24
  10. 24
  11. 28
  12. 24
  13. 120
  14. 49
  15. 55
  16. 6
  17. 36
  18. 30
  19. 20
  20. 9
  21. 30
  22. 15
  23. 12
  24. 120
  25. 72
  26. 105
  27. 6
  28. 15
  29. 28
  30. 105
  31. 66
  32. 110
  33. 24
  34. 21
  35. 20
  36. 20
  37. 6
  38. 48
  39. 91
  40. 15

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