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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 335 · 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.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 90 (c) 100 (d) 20
  2. 2.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 5 (c) 6 (d) 12
  3. 3.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 110 (c) 66 (d) 121
  4. 4.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 144 (c) 24 (d) 132
  5. 5.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 55 (d) 90
  6. 6.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 90 (c) 100 (d) 55
  7. 7.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
  8. 8.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
  9. 9.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  10. 10.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 36 (d) 45
  11. 11.8 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) 15 (b) 112 (c) 64 (d) 56
  12. 12.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 56 (d) 28
  13. 13.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  14. 14.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) 10 (c) 20 (d) 15
  15. 15.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 225 (c) 210 (d) 120
  16. 16.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  17. 17.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 12 (d) 15
  18. 18.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 110 (d) 55
  19. 19.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  20. 20.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 9 (c) 12 (d) 6
  21. 21.There are 7 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) 49 (b) 84 (c) 42 (d) 13
  22. 22.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 105 (d) 91
  23. 23.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) 42 (d) 21
  24. 24.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 169 (c) 156 (d) 78
  25. 25.8 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) 48 (b) 14 (c) 96 (d) 56
  26. 26.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 105 (c) 210 (d) 225
  27. 27.4 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) 7 (b) 12 (c) 24 (d) 16
  28. 28.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  29. 29.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 21 (d) 49
  30. 30.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 81 (d) 45
  31. 31.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  32. 32.5 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) 40 (b) 70 (c) 12 (d) 35
  33. 33.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 72 (c) 81 (d) 18
  34. 34.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  35. 35.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  36. 36.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 56 (c) 64 (d) 28
  37. 37.6 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) 84 (b) 13 (c) 48 (d) 42
  38. 38.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  39. 39.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 28 (c) 16 (d) 56
  40. 40.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) 24 (b) 48 (c) 30 (d) 10

Answer key

  1. 90
  2. 6
  3. 55
  4. 132
  5. 45
  6. 45
  7. 10
  8. 21
  9. 6
  10. 36
  11. 56
  12. 28
  13. 120
  14. 10
  15. 105
  16. 24
  17. 15
  18. 55
  19. 24
  20. 9
  21. 42
  22. 91
  23. 42
  24. 78
  25. 48
  26. 105
  27. 12
  28. 120
  29. 21
  30. 36
  31. 120
  32. 35
  33. 36
  34. 6
  35. 24
  36. 28
  37. 42
  38. 6
  39. 56
  40. 24

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