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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 239 · 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).

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  1. 1.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  2. 2.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 30 (d) 15
  3. 3.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 64 (c) 36 (d) 28
  4. 4.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  5. 5.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) 6 (c) 8 (d) 16
  6. 6.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 121 (d) 55
  7. 7.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 15 (c) 10 (d) 25
  8. 8.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 36 (c) 56 (d) 64
  9. 9.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 11 (d) 10
  10. 10.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  11. 11.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) 32 (b) 48 (c) 24 (d) 11
  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) 110 (c) 22 (d) 121
  13. 13.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) 10 (c) 25 (d) 50
  14. 14.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 144 (d) 66
  15. 15.7 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) 70 (b) 35 (c) 42 (d) 12
  16. 16.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 36 (d) 15
  17. 17.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 81 (c) 36 (d) 45
  18. 18.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) 35 (b) 12 (c) 42 (d) 70
  19. 19.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 45 (c) 90 (d) 20
  20. 20.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  21. 21.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 16 (d) 28
  22. 22.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 10 (d) 25
  23. 23.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  24. 24.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 55 (c) 100 (d) 90
  25. 25.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) 36 (d) 72
  26. 26.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 10 (d) 20
  27. 27.There are 4 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) 24 (b) 9 (c) 40 (d) 20
  28. 28.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 121 (d) 55
  29. 29.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 14 (b) 98 (c) 49 (d) 56
  30. 30.6 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) 13 (b) 48 (c) 42 (d) 84
  31. 31.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 144 (d) 132
  32. 32.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 16 (c) 64 (d) 56
  33. 33.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 45 (c) 20 (d) 90
  34. 34.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 91 (d) 105
  35. 35.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 21 (d) 49
  36. 36.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  37. 37.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) 24 (b) 42 (c) 10 (d) 21
  38. 38.7 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) 84 (c) 13 (d) 49
  39. 39.8 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) 10 (d) 24
  40. 40.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) 28 (b) 21 (c) 14 (d) 9

Answer key

  1. 6
  2. 30
  3. 28
  4. 24
  5. 8
  6. 55
  7. 10
  8. 28
  9. 10
  10. 24
  11. 24
  12. 110
  13. 25
  14. 66
  15. 35
  16. 15
  17. 36
  18. 35
  19. 45
  20. 120
  21. 56
  22. 10
  23. 120
  24. 45
  25. 72
  26. 20
  27. 20
  28. 55
  29. 49
  30. 42
  31. 66
  32. 28
  33. 90
  34. 91
  35. 21
  36. 120
  37. 21
  38. 42
  39. 16
  40. 14

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