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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 322 · 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.There are 7 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) 9 (b) 28 (c) 21 (d) 14
  2. 2.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  3. 3.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  4. 4.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 182 (c) 105 (d) 91
  5. 5.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 100 (d) 45
  6. 6.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 21 (c) 28 (d) 42
  7. 7.15 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
  8. 8.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 24 (c) 10 (d) 30
  9. 9.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 196 (c) 105 (d) 182
  10. 10.4 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) 40 (c) 9 (d) 24
  11. 11.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) 56 (b) 98 (c) 14 (d) 49
  12. 12.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 156 (d) 169
  13. 13.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  14. 14.There are 8 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) 11 (b) 32 (c) 24 (d) 48
  15. 15.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) 8 (d) 15
  16. 16.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  17. 17.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  18. 18.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 11 (d) 25
  19. 19.There are 3 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) 9 (b) 5 (c) 6 (d) 12
  20. 20.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 100 (c) 90 (d) 55
  21. 21.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 81 (d) 36
  22. 22.8 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) 40 (b) 64 (c) 12 (d) 32
  23. 23.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) 12 (b) 15 (c) 7 (d) 24
  24. 24.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 10 (d) 20
  25. 25.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  26. 26.There are 5 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) 25 (b) 10 (c) 50 (d) 30
  27. 27.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) 49 (d) 42
  28. 28.6 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) 18 (b) 24 (c) 8 (d) 12
  29. 29.7 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) 9 (b) 21 (c) 14 (d) 28
  30. 30.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 32 (c) 16 (d) 8
  31. 31.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 66 (d) 132
  32. 32.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 144 (c) 78 (d) 132
  33. 33.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 10 (c) 20 (d) 25
  34. 34.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 28 (d) 49
  35. 35.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 81 (c) 45 (d) 36
  36. 36.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
  37. 37.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  38. 38.5 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) 25 (c) 10 (d) 30
  39. 39.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  40. 40.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 210 (c) 120 (d) 225

Answer key

  1. 14
  2. 120
  3. 24
  4. 91
  5. 45
  6. 21
  7. 105
  8. 24
  9. 91
  10. 20
  11. 49
  12. 78
  13. 120
  14. 24
  15. 15
  16. 24
  17. 120
  18. 10
  19. 6
  20. 45
  21. 72
  22. 32
  23. 12
  24. 20
  25. 6
  26. 25
  27. 42
  28. 12
  29. 14
  30. 16
  31. 66
  32. 66
  33. 10
  34. 21
  35. 36
  36. 21
  37. 24
  38. 25
  39. 120
  40. 105

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