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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 753 · 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) 9 (c) 12 (d) 6
  2. 2.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 30 (d) 21
  3. 3.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) 90 (d) 20
  4. 4.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  5. 5.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) 9 (c) 21 (d) 14
  6. 6.14 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
  7. 7.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  8. 8.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 18 (c) 81 (d) 72
  9. 9.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 42 (d) 49
  10. 10.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 110 (c) 66 (d) 121
  11. 11.11 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
  12. 12.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 100 (d) 45
  13. 13.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 64 (c) 16 (d) 56
  14. 14.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  15. 15.4 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) 12 (b) 6 (c) 16 (d) 8
  16. 16.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  17. 17.3 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) 24 (b) 15 (c) 7 (d) 12
  18. 18.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  19. 19.8 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) 48 (b) 32 (c) 24 (d) 11
  20. 20.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 21 (c) 9 (d) 18
  21. 21.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 45 (c) 55 (d) 100
  22. 22.4 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) 20 (b) 9 (c) 24 (d) 40
  23. 23.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) 9 (b) 24 (c) 20 (d) 40
  24. 24.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 42 (d) 21
  25. 25.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) 11 (b) 36 (c) 60 (d) 30
  26. 26.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 36 (c) 45 (d) 72
  27. 27.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 10 (d) 20
  28. 28.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
  29. 29.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  30. 30.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) 24 (b) 8 (c) 12 (d) 18
  31. 31.6 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) 84 (d) 42
  32. 32.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 169 (c) 156 (d) 91
  33. 33.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 15 (c) 7 (d) 12
  34. 34.7 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) 49 (b) 42 (c) 13 (d) 84
  35. 35.3 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) 9 (c) 6 (d) 12
  36. 36.8 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) 13 (b) 48 (c) 80 (d) 40
  37. 37.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 15 (c) 30 (d) 36
  38. 38.6 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) 11 (b) 30 (c) 60 (d) 36
  39. 39.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  40. 40.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 10 (c) 21 (d) 20

Answer key

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

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