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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 110 · 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 4 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) 7 (b) 16 (c) 12 (d) 24
  2. 2.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 100 (c) 55 (d) 45
  3. 3.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 105 (d) 225
  4. 4.4 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) 48 (b) 24 (c) 28 (d) 10
  5. 5.6 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) 8 (c) 18 (d) 24
  6. 6.4 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) 16 (b) 6 (c) 8 (d) 12
  7. 7.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  8. 8.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
  9. 9.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 56 (c) 28 (d) 64
  10. 10.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  11. 11.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 36 (c) 18 (d) 81
  12. 12.3 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) 18 (b) 9 (c) 6 (d) 12
  13. 13.6 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) 18 (b) 24 (c) 9 (d) 36
  14. 14.4 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) 9 (b) 24 (c) 40 (d) 20
  15. 15.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  16. 16.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  17. 17.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
  18. 18.There are 6 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) 10 (b) 48 (c) 30 (d) 24
  19. 19.5 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) 30 (b) 25 (c) 10 (d) 50
  20. 20.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  21. 21.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 15 (d) 21
  22. 22.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) 21 (b) 28 (c) 10 (d) 42
  23. 23.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 105 (d) 91
  24. 24.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 64 (b) 112 (c) 15 (d) 56
  25. 25.6 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) 84 (b) 13 (c) 48 (d) 42
  26. 26.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  27. 27.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  28. 28.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 20 (c) 90 (d) 100
  29. 29.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
  30. 30.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 90 (d) 45
  31. 31.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  32. 32.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 78 (c) 169 (d) 91
  33. 33.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 121 (c) 55 (d) 110
  34. 34.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  35. 35.There are 7 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) 11 (b) 35 (c) 56 (d) 28
  36. 36.8 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) 112 (b) 15 (c) 56 (d) 64
  37. 37.4 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) 8 (b) 32 (c) 16 (d) 20
  38. 38.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 42 (c) 49 (d) 14
  39. 39.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 110 (d) 121
  40. 40.3 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) 9 (c) 5 (d) 6

Answer key

  1. 12
  2. 45
  3. 105
  4. 24
  5. 12
  6. 8
  7. 120
  8. 28
  9. 28
  10. 120
  11. 72
  12. 9
  13. 18
  14. 20
  15. 24
  16. 24
  17. 15
  18. 24
  19. 25
  20. 120
  21. 15
  22. 21
  23. 91
  24. 56
  25. 42
  26. 24
  27. 6
  28. 45
  29. 10
  30. 90
  31. 6
  32. 78
  33. 55
  34. 24
  35. 28
  36. 56
  37. 16
  38. 21
  39. 110
  40. 6

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