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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 785 · 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 10 players. How many different teams are possible? (a) 45 (b) 100 (c) 20 (d) 90
  2. 2.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 14 (c) 42 (d) 21
  3. 3.3 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
  4. 4.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 15 (d) 30
  5. 5.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  6. 6.There are 6 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) 24 (b) 12 (c) 8 (d) 18
  7. 7.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  8. 8.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 78 (c) 132 (d) 144
  9. 9.8 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) 96 (b) 14 (c) 48 (d) 56
  10. 10.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  11. 11.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55
  12. 12.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 14 (c) 42 (d) 49
  13. 13.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 110 (c) 22 (d) 121
  14. 14.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) 48 (b) 28 (c) 24 (d) 10
  15. 15.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) 21 (b) 24 (c) 10 (d) 42
  16. 16.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 15 (d) 36
  17. 17.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 98 (b) 49 (c) 56 (d) 14
  18. 18.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) 12 (b) 7 (c) 15 (d) 24
  19. 19.6 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) 60 (c) 36 (d) 30
  20. 20.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
  21. 21.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 105 (c) 225 (d) 210
  22. 22.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  23. 23.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  24. 24.4 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) 28 (b) 24 (c) 48 (d) 10
  25. 25.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  26. 26.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 105 (d) 182
  27. 27.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  28. 28.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 55 (c) 22 (d) 110
  29. 29.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) 9 (b) 12 (c) 18 (d) 6
  30. 30.4 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) 9 (b) 40 (c) 24 (d) 20
  31. 31.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 64 (c) 56 (d) 36
  32. 32.7 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) 10 (b) 28 (c) 42 (d) 21
  33. 33.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) 70 (b) 35 (c) 12 (d) 42
  34. 34.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  35. 35.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 20 (d) 10
  36. 36.5 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) 30 (b) 35 (c) 60 (d) 11
  37. 37.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  38. 38.4 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) 8 (b) 20 (c) 32 (d) 16
  39. 39.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) 20 (b) 8 (c) 15 (d) 30
  40. 40.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 28 (d) 64

Answer key

  1. 45
  2. 21
  3. 6
  4. 15
  5. 24
  6. 12
  7. 24
  8. 66
  9. 48
  10. 120
  11. 55
  12. 42
  13. 55
  14. 24
  15. 21
  16. 15
  17. 49
  18. 12
  19. 30
  20. 10
  21. 105
  22. 6
  23. 24
  24. 24
  25. 120
  26. 91
  27. 6
  28. 110
  29. 9
  30. 20
  31. 28
  32. 21
  33. 35
  34. 120
  35. 10
  36. 30
  37. 24
  38. 16
  39. 15
  40. 28

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