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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 958 · 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 PEN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  2. 2.3 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
  3. 3.4 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) 10 (b) 48 (c) 24 (d) 28
  4. 4.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) 35 (b) 28 (c) 11 (d) 56
  5. 5.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
  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) 13 (b) 40 (c) 80 (d) 48
  7. 7.4 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) 28 (c) 32 (d) 11
  8. 8.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 55 (c) 110 (d) 66
  9. 9.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
  10. 10.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) 35 (b) 56 (c) 28 (d) 11
  11. 11.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 10 (c) 25 (d) 11
  12. 12.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) 16 (b) 12 (c) 8 (d) 6
  13. 13.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) 48 (b) 96 (c) 56 (d) 14
  14. 14.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) 48 (b) 13 (c) 42 (d) 84
  15. 15.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 55 (c) 66 (d) 121
  16. 16.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
  17. 17.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  18. 18.8 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) 32 (b) 24 (c) 48 (d) 11
  19. 19.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 36 (c) 18 (d) 72
  20. 20.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  21. 21.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 55 (d) 45
  22. 22.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 49 (d) 42
  23. 23.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 42 (c) 21 (d) 49
  24. 24.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 15 (d) 36
  25. 25.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 66 (c) 78 (d) 144
  26. 26.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 20 (c) 100 (d) 45
  27. 27.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 91 (c) 105 (d) 182
  28. 28.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  29. 29.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  30. 30.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 36 (c) 81 (d) 72
  31. 31.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  32. 32.8 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) 48 (b) 40 (c) 13 (d) 80
  33. 33.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) 7 (b) 20 (c) 15 (d) 10
  34. 34.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 25 (d) 10
  35. 35.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  36. 36.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) 81 (d) 18
  37. 37.There are 6 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) 72 (b) 12 (c) 42 (d) 36
  38. 38.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) 8 (b) 15 (c) 20 (d) 30
  39. 39.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 21 (d) 49
  40. 40.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 240 (d) 20

Answer key

  1. 6
  2. 6
  3. 24
  4. 28
  5. 36
  6. 40
  7. 28
  8. 55
  9. 15
  10. 28
  11. 10
  12. 8
  13. 48
  14. 42
  15. 55
  16. 28
  17. 24
  18. 24
  19. 36
  20. 120
  21. 45
  22. 21
  23. 42
  24. 15
  25. 66
  26. 90
  27. 91
  28. 6
  29. 24
  30. 36
  31. 24
  32. 40
  33. 10
  34. 10
  35. 6
  36. 72
  37. 36
  38. 15
  39. 21
  40. 120

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