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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 34 · 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.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 15 (d) 30
  2. 2.6 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) 24 (b) 36 (c) 9 (d) 18
  3. 3.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 21 (c) 25 (d) 10
  4. 4.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  5. 5.There are 6 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) 60 (b) 11 (c) 30 (d) 36
  6. 6.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) 25 (b) 20 (c) 9 (d) 40
  7. 7.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) 42 (b) 28 (c) 10 (d) 21
  8. 8.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  9. 9.3 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) 9 (b) 36 (c) 21 (d) 18
  10. 10.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 66 (d) 78
  11. 11.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 66 (d) 144
  12. 12.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) 121 (d) 110
  13. 13.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
  14. 14.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 9 (c) 18 (d) 24
  15. 15.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  16. 16.3 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) 5 (b) 12 (c) 6 (d) 9
  17. 17.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  18. 18.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 45 (c) 100 (d) 20
  19. 19.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 21 (c) 14 (d) 49
  20. 20.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 28 (c) 64 (d) 56
  21. 21.3 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) 12 (b) 18 (c) 6 (d) 9
  22. 22.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 15 (d) 36
  23. 23.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  24. 24.6 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) 18 (c) 24 (d) 8
  25. 25.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 9 (c) 14 (d) 28
  26. 26.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 20 (d) 10
  27. 27.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 105 (d) 120
  28. 28.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 6 (d) 3
  29. 29.There are 5 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) 25 (b) 30 (c) 50 (d) 10
  30. 30.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 81 (c) 72 (d) 45
  31. 31.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 36 (c) 81 (d) 72
  32. 32.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  33. 33.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 156 (c) 78 (d) 169
  34. 34.There are 6 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) 18 (c) 8 (d) 12
  35. 35.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 49 (c) 42 (d) 28
  36. 36.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 55 (d) 110
  37. 37.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) 16 (b) 24 (c) 10 (d) 32
  38. 38.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55
  39. 39.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) 112 (b) 64 (c) 56 (d) 15
  40. 40.5 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) 35 (b) 30 (c) 60 (d) 11

Answer key

  1. 15
  2. 18
  3. 20
  4. 6
  5. 30
  6. 20
  7. 21
  8. 120
  9. 18
  10. 66
  11. 66
  12. 110
  13. 45
  14. 18
  15. 24
  16. 6
  17. 120
  18. 45
  19. 42
  20. 28
  21. 9
  22. 15
  23. 120
  24. 12
  25. 14
  26. 10
  27. 105
  28. 6
  29. 25
  30. 36
  31. 72
  32. 6
  33. 78
  34. 12
  35. 21
  36. 55
  37. 16
  38. 55
  39. 56
  40. 30

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