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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 74 · 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 SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  2. 2.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 66 (d) 132
  3. 3.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 11 (c) 28 (d) 56
  4. 4.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 22 (c) 121 (d) 110
  5. 5.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
  6. 6.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 20 (c) 10 (d) 25
  7. 7.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  8. 8.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 64 (c) 28 (d) 36
  9. 9.4 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) 16 (b) 12 (c) 6 (d) 8
  10. 10.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) 21 (d) 42
  11. 11.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 10 (d) 20
  12. 12.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 12 (d) 15
  13. 13.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 45 (c) 20 (d) 100
  14. 14.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 12 (c) 70 (d) 35
  15. 15.5 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) 50 (b) 10 (c) 25 (d) 30
  16. 16.3 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) 7 (b) 15 (c) 24 (d) 12
  17. 17.6 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) 24 (c) 18 (d) 8
  18. 18.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
  19. 19.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  20. 20.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 144 (c) 78 (d) 132
  21. 21.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) 98 (b) 14 (c) 56 (d) 49
  22. 22.There are 3 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) 8 (b) 18 (c) 15 (d) 30
  23. 23.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 45 (c) 36 (d) 81
  24. 24.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 72 (d) 36
  25. 25.6 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) 60 (b) 30 (c) 36 (d) 11
  26. 26.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 55 (c) 22 (d) 121
  27. 27.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 66 (c) 78 (d) 144
  28. 28.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 12 (d) 9
  29. 29.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  30. 30.There are 3 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) 15 (b) 7 (c) 24 (d) 12
  31. 31.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 49 (d) 28
  32. 32.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) 12 (b) 72 (c) 36 (d) 42
  33. 33.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  34. 34.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 15 (c) 25 (d) 10
  35. 35.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 169 (c) 91 (d) 156
  36. 36.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  37. 37.8 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) 56 (c) 112 (d) 64
  38. 38.7 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
  39. 39.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 210 (c) 120 (d) 225
  40. 40.There are 3 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) 6 (b) 9 (c) 12 (d) 18

Answer key

  1. 6
  2. 132
  3. 28
  4. 55
  5. 28
  6. 10
  7. 6
  8. 28
  9. 8
  10. 42
  11. 10
  12. 30
  13. 45
  14. 35
  15. 25
  16. 12
  17. 12
  18. 21
  19. 120
  20. 66
  21. 49
  22. 15
  23. 36
  24. 36
  25. 30
  26. 110
  27. 66
  28. 6
  29. 24
  30. 12
  31. 21
  32. 36
  33. 120
  34. 10
  35. 78
  36. 24
  37. 56
  38. 21
  39. 105
  40. 9

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