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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 585 · 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 LAMP be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  2. 2.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 105 (c) 196 (d) 91
  3. 3.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 28 (c) 56 (d) 36
  4. 4.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 25 (c) 20 (d) 10
  5. 5.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 36 (c) 18 (d) 24
  6. 6.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  7. 7.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  8. 8.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  9. 9.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 30 (d) 15
  10. 10.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 45 (d) 36
  11. 11.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 49 (c) 14 (d) 21
  12. 12.6 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) 42 (b) 72 (c) 12 (d) 36
  13. 13.There are 4 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) 32 (b) 11 (c) 28 (d) 56
  14. 14.4 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) 10 (d) 48
  15. 15.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 14 (c) 21 (d) 28
  16. 16.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 132 (d) 144
  17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  18. 18.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  19. 19.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 64 (c) 56 (d) 16
  20. 20.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 66 (d) 132
  21. 21.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 132 (c) 24 (d) 144
  22. 22.There are 4 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) 7 (b) 16 (c) 24 (d) 12
  23. 23.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 55 (c) 121 (d) 110
  24. 24.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 28 (c) 21 (d) 42
  25. 25.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 25 (d) 15
  26. 26.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
  27. 27.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 36 (d) 72
  28. 28.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 12 (c) 36 (d) 30
  29. 29.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  30. 30.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  31. 31.4 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) 24 (b) 20 (c) 40 (d) 9
  32. 32.6 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) 12 (d) 8
  33. 33.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
  34. 34.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 10 (c) 15 (d) 20
  35. 35.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 120 (c) 210 (d) 105
  36. 36.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  37. 37.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  38. 38.15 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
  39. 39.There are 4 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) 8 (b) 20 (c) 32 (d) 16
  40. 40.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 144 (c) 66 (d) 132

Answer key

  1. 24
  2. 91
  3. 28
  4. 20
  5. 18
  6. 120
  7. 6
  8. 6
  9. 15
  10. 36
  11. 42
  12. 36
  13. 28
  14. 24
  15. 14
  16. 66
  17. 24
  18. 120
  19. 56
  20. 66
  21. 132
  22. 12
  23. 110
  24. 21
  25. 10
  26. 72
  27. 36
  28. 15
  29. 120
  30. 120
  31. 20
  32. 12
  33. 9
  34. 10
  35. 105
  36. 24
  37. 6
  38. 105
  39. 16
  40. 66

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