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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 65 · 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 5 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) 15 (b) 20 (c) 30 (d) 8
  2. 2.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 15 (d) 25
  3. 3.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 21 (d) 30
  4. 4.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
  5. 5.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  6. 6.6 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) 48 (c) 30 (d) 24
  7. 7.There are 5 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) 10 (b) 15 (c) 20 (d) 7
  8. 8.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  9. 9.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 30 (d) 15
  10. 10.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 110 (d) 55
  11. 11.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  12. 12.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 21 (c) 49 (d) 14
  13. 13.6 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) 12 (b) 24 (c) 18 (d) 8
  14. 14.There are 7 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) 21 (b) 9 (c) 14 (d) 28
  15. 15.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  16. 16.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 90 (c) 100 (d) 55
  17. 17.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  18. 18.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 78 (d) 91
  19. 19.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) 28 (c) 48 (d) 24
  20. 20.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) 32 (d) 28
  21. 21.There are 6 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) 84 (b) 13 (c) 42 (d) 48
  22. 22.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 144 (d) 66
  23. 23.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  24. 24.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  25. 25.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 105 (d) 210
  26. 26.6 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) 36 (b) 72 (c) 12 (d) 42
  27. 27.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) 56 (b) 28 (c) 11 (d) 35
  28. 28.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 45 (c) 72 (d) 81
  29. 29.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) 24 (b) 48 (c) 28 (d) 10
  30. 30.7 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) 42 (b) 13 (c) 49 (d) 84
  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) 12 (b) 6 (c) 5 (d) 9
  32. 32.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
  33. 33.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
  34. 34.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 45 (c) 20 (d) 100
  35. 35.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 42 (c) 14 (d) 21
  36. 36.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) 12 (b) 16 (c) 7 (d) 24
  37. 37.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 10 (d) 11
  38. 38.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
  39. 39.6 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
  40. 40.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 48 (d) 12

Answer key

  1. 15
  2. 10
  3. 15
  4. 72
  5. 24
  6. 24
  7. 10
  8. 24
  9. 30
  10. 110
  11. 120
  12. 21
  13. 12
  14. 14
  15. 120
  16. 45
  17. 6
  18. 78
  19. 24
  20. 28
  21. 42
  22. 66
  23. 6
  24. 24
  25. 105
  26. 36
  27. 28
  28. 36
  29. 24
  30. 42
  31. 6
  32. 45
  33. 15
  34. 90
  35. 42
  36. 12
  37. 10
  38. 6
  39. 15
  40. 24

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