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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 97 · 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. 1.8 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) 32 (b) 16 (c) 24 (d) 10
  2. 2.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 12 (c) 36 (d) 15
  3. 3.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 90 (d) 45
  4. 4.5 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) 25 (b) 30 (c) 10 (d) 50
  5. 5.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 90 (c) 55 (d) 100
  6. 6.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) 32 (c) 48 (d) 11
  7. 7.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  8. 8.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 49 (d) 42
  9. 9.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 132 (d) 78
  10. 10.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 21 (d) 30
  11. 11.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 81 (d) 72
  12. 12.6 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) 30 (c) 24 (d) 48
  13. 13.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  14. 14.5 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) 40 (b) 20 (c) 9 (d) 25
  15. 15.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 12 (c) 8 (d) 24
  16. 16.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) 32 (b) 11 (c) 56 (d) 28
  17. 17.There are 7 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) 42 (b) 12 (c) 35 (d) 70
  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) 30 (b) 48 (c) 10 (d) 24
  19. 19.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 10 (d) 15
  20. 20.4 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) 40 (c) 24 (d) 20
  21. 21.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) 56 (b) 112 (c) 15 (d) 64
  22. 22.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) 100 (d) 45
  23. 23.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 8 (c) 6 (d) 16
  24. 24.13 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
  25. 25.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 66 (d) 144
  26. 26.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 50 (c) 25 (d) 10
  27. 27.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) 24 (d) 20
  28. 28.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 55 (c) 110 (d) 121
  29. 29.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
  30. 30.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) 42 (b) 10 (c) 21 (d) 28
  31. 31.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 21 (d) 42
  32. 32.7 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) 49 (c) 98 (d) 14
  33. 33.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  34. 34.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  35. 35.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) 10 (b) 24 (c) 21 (d) 42
  36. 36.7 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) 14 (b) 21 (c) 28 (d) 9
  37. 37.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 210 (c) 120 (d) 225
  38. 38.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  39. 39.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) 9 (b) 36 (c) 24 (d) 18
  40. 40.5 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

Answer key

  1. 16
  2. 30
  3. 45
  4. 25
  5. 45
  6. 24
  7. 120
  8. 21
  9. 66
  10. 15
  11. 72
  12. 24
  13. 6
  14. 20
  15. 12
  16. 28
  17. 35
  18. 24
  19. 10
  20. 20
  21. 56
  22. 90
  23. 8
  24. 78
  25. 66
  26. 25
  27. 20
  28. 110
  29. 15
  30. 21
  31. 42
  32. 49
  33. 120
  34. 120
  35. 21
  36. 14
  37. 105
  38. 24
  39. 18
  40. 10

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