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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 23 · 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.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) 48 (c) 32 (d) 11
  2. 2.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 110 (c) 66 (d) 55
  3. 3.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  4. 4.8 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) 64 (c) 112 (d) 15
  5. 5.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  6. 6.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 24 (c) 144 (d) 66
  7. 7.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  8. 8.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 35 (c) 30 (d) 11
  9. 9.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  10. 10.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 105 (d) 196
  11. 11.3 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) 18 (b) 9 (c) 21 (d) 36
  12. 12.3 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) 21 (b) 42 (c) 10 (d) 24
  13. 13.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 81 (c) 72 (d) 36
  14. 14.8 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) 48 (b) 96 (c) 56 (d) 14
  15. 15.3 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) 15 (c) 30 (d) 8
  16. 16.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 14 (c) 49 (d) 98
  17. 17.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 21 (c) 28 (d) 42
  18. 18.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 210 (c) 105 (d) 225
  19. 19.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 25 (c) 15 (d) 20
  20. 20.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 10 (c) 25 (d) 20
  21. 21.8 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) 11 (b) 24 (c) 48 (d) 32
  22. 22.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 110 (d) 55
  23. 23.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 21 (d) 49
  24. 24.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 9 (c) 12 (d) 18
  25. 25.There are 7 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) 28 (b) 10 (c) 21 (d) 42
  26. 26.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  27. 27.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 18 (c) 9 (d) 36
  28. 28.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) 8 (b) 30 (c) 15 (d) 18
  29. 29.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 144 (d) 24
  30. 30.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 28 (d) 64
  31. 31.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  32. 32.There are 6 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) 9 (c) 36 (d) 18
  33. 33.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 24 (c) 20 (d) 40
  34. 34.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 90 (d) 100
  35. 35.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) 42 (b) 12 (c) 72 (d) 36
  36. 36.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 225 (c) 105 (d) 120
  37. 37.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  38. 38.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 64 (d) 36
  39. 39.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 45 (d) 20
  40. 40.4 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) 20 (b) 16 (c) 8 (d) 32

Answer key

  1. 24
  2. 55
  3. 24
  4. 56
  5. 6
  6. 132
  7. 120
  8. 30
  9. 6
  10. 91
  11. 18
  12. 21
  13. 36
  14. 48
  15. 15
  16. 49
  17. 21
  18. 105
  19. 10
  20. 10
  21. 24
  22. 55
  23. 21
  24. 9
  25. 21
  26. 24
  27. 18
  28. 15
  29. 66
  30. 28
  31. 120
  32. 18
  33. 20
  34. 90
  35. 36
  36. 105
  37. 24
  38. 28
  39. 45
  40. 16

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