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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 595 · 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.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  2. 2.7 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) 28 (c) 21 (d) 14
  3. 3.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  4. 4.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) 9 (b) 25 (c) 40 (d) 20
  5. 5.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 28 (d) 56
  6. 6.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) 80 (c) 48 (d) 13
  7. 7.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 132 (d) 144
  8. 8.3 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) 36 (b) 9 (c) 21 (d) 18
  9. 9.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  10. 10.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 64 (c) 28 (d) 56
  11. 11.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) 30 (b) 18 (c) 15 (d) 8
  12. 12.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 90 (c) 45 (d) 100
  13. 13.There are 5 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) 11 (b) 30 (c) 35 (d) 60
  14. 14.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) 14 (b) 98 (c) 56 (d) 49
  15. 15.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 22 (d) 110
  16. 16.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  17. 17.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 55 (c) 45 (d) 90
  18. 18.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 55 (d) 121
  19. 19.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 20 (d) 10
  20. 20.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) 7 (b) 16 (c) 24 (d) 12
  21. 21.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
  22. 22.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 81 (c) 45 (d) 36
  23. 23.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 70 (c) 42 (d) 12
  24. 24.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 24 (d) 132
  25. 25.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  26. 26.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 36 (d) 15
  27. 27.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 64 (c) 56 (d) 16
  28. 28.There are 7 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) 84 (b) 49 (c) 13 (d) 42
  29. 29.7 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) 42 (b) 35 (c) 12 (d) 70
  30. 30.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) 14 (b) 96 (c) 56 (d) 48
  31. 31.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 32 (c) 16 (d) 8
  32. 32.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 64 (c) 32 (d) 40
  33. 33.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 25 (c) 20 (d) 10
  34. 34.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  35. 35.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  36. 36.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 6 (d) 3
  37. 37.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) 36 (b) 9 (c) 18 (d) 21
  38. 38.6 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) 30 (b) 24 (c) 48 (d) 10
  39. 39.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 14 (c) 49 (d) 42
  40. 40.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 20 (d) 45

Answer key

  1. 6
  2. 14
  3. 24
  4. 20
  5. 56
  6. 40
  7. 132
  8. 18
  9. 120
  10. 28
  11. 15
  12. 90
  13. 30
  14. 49
  15. 55
  16. 24
  17. 45
  18. 110
  19. 10
  20. 12
  21. 48
  22. 36
  23. 35
  24. 66
  25. 24
  26. 15
  27. 28
  28. 42
  29. 35
  30. 48
  31. 16
  32. 32
  33. 10
  34. 6
  35. 24
  36. 6
  37. 18
  38. 24
  39. 21
  40. 45

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