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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 723 · 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 3 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) 12 (b) 5 (c) 9 (d) 6
  2. 2.There are 8 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) 24 (b) 32 (c) 10 (d) 16
  3. 3.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 32 (c) 28 (d) 11
  4. 4.7 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
  5. 5.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 66 (c) 110 (d) 55
  6. 6.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) 24 (c) 21 (d) 10
  7. 7.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  8. 8.There are 3 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) 18 (b) 36 (c) 9 (d) 21
  9. 9.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) 40 (b) 9 (c) 20 (d) 24
  10. 10.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 55 (c) 90 (d) 45
  11. 11.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) 18 (b) 24 (c) 9 (d) 36
  12. 12.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 210 (c) 225 (d) 120
  13. 13.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  14. 14.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 81 (d) 45
  15. 15.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  16. 16.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  17. 17.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  18. 18.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
  19. 19.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 13 (c) 84 (d) 49
  20. 20.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  21. 21.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  22. 22.There are 4 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) 11 (b) 56 (c) 28 (d) 32
  23. 23.4 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) 32 (c) 8 (d) 16
  24. 24.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 20 (d) 25
  25. 25.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  26. 26.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  27. 27.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  28. 28.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 21 (c) 30 (d) 36
  29. 29.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 81 (c) 72 (d) 36
  30. 30.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 28 (c) 42 (d) 21
  31. 31.3 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) 5 (d) 12
  32. 32.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  33. 33.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 36 (c) 72 (d) 81
  34. 34.4 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) 24 (b) 10 (c) 48 (d) 28
  35. 35.6 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) 12 (b) 72 (c) 42 (d) 36
  36. 36.There are 3 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) 8 (b) 18 (c) 30 (d) 15
  37. 37.There are 4 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) 16 (b) 8 (c) 32 (d) 20
  38. 38.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) 48 (b) 28 (c) 24 (d) 10
  39. 39.6 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) 10 (b) 24 (c) 30 (d) 48
  40. 40.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

Answer key

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

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