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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 411 · 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 team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 21 (c) 49 (d) 14
  2. 2.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 90 (d) 45
  3. 3.5 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) 11 (b) 35 (c) 30 (d) 60
  4. 4.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
  5. 5.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 70 (c) 40 (d) 35
  6. 6.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  7. 7.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 15 (d) 30
  8. 8.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
  9. 9.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
  10. 10.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 132 (d) 144
  11. 11.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  12. 12.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  13. 13.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  14. 14.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) 30 (c) 20 (d) 15
  15. 15.There are 4 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) 28 (b) 48 (c) 24 (d) 10
  16. 16.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 64 (c) 28 (d) 56
  17. 17.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) 18 (b) 12 (c) 9 (d) 6
  18. 18.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 66 (d) 24
  19. 19.7 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
  20. 20.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
  21. 21.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) 30 (b) 24 (c) 10 (d) 48
  22. 22.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 144 (d) 66
  23. 23.7 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) 28 (b) 14 (c) 21 (d) 9
  24. 24.5 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) 30 (c) 25 (d) 10
  25. 25.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 18 (c) 15 (d) 8
  26. 26.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 105 (c) 225 (d) 120
  27. 27.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 121 (d) 55
  28. 28.5 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
  29. 29.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) 15 (d) 12
  30. 30.3 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) 21 (b) 36 (c) 9 (d) 18
  31. 31.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  32. 32.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 25 (d) 21
  33. 33.4 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) 32 (b) 28 (c) 56 (d) 11
  34. 34.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
  35. 35.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 91 (d) 182
  36. 36.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 36 (d) 18
  37. 37.8 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) 80 (c) 40 (d) 48
  38. 38.3 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) 42 (b) 10 (c) 24 (d) 21
  39. 39.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 91 (d) 182
  40. 40.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 90 (d) 45

Answer key

  1. 21
  2. 45
  3. 30
  4. 48
  5. 35
  6. 120
  7. 15
  8. 72
  9. 6
  10. 132
  11. 120
  12. 120
  13. 6
  14. 15
  15. 24
  16. 28
  17. 9
  18. 66
  19. 21
  20. 15
  21. 24
  22. 66
  23. 14
  24. 25
  25. 15
  26. 105
  27. 110
  28. 10
  29. 30
  30. 18
  31. 120
  32. 20
  33. 28
  34. 15
  35. 91
  36. 36
  37. 40
  38. 21
  39. 91
  40. 90

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