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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 135 · 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 MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  2. 2.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  3. 3.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 30 (d) 15
  4. 4.There are 6 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) 24 (c) 18 (d) 36
  5. 5.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 11 (c) 30 (d) 35
  6. 6.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 10 (c) 15 (d) 25
  7. 7.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 30 (d) 12
  8. 8.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 11 (c) 24 (d) 32
  9. 9.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 30 (d) 21
  10. 10.7 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) 28 (b) 42 (c) 10 (d) 21
  11. 11.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 16 (d) 64
  12. 12.7 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
  13. 13.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 110 (c) 66 (d) 55
  14. 14.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) 8 (b) 30 (c) 15 (d) 18
  15. 15.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 42 (d) 21
  16. 16.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  17. 17.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  18. 18.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  19. 19.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 10 (d) 11
  20. 20.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 10 (d) 15
  21. 21.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  22. 22.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 42 (c) 28 (d) 49
  23. 23.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) 12 (b) 6 (c) 5 (d) 9
  24. 24.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 12 (c) 18 (d) 8
  25. 25.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 225 (c) 120 (d) 210
  26. 26.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 132 (d) 144
  27. 27.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  28. 28.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 169 (c) 156 (d) 78
  29. 29.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 36 (c) 28 (d) 64
  30. 30.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
  31. 31.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 196 (d) 105
  32. 32.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 22 (d) 55
  33. 33.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) 36 (c) 42 (d) 72
  34. 34.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) 10 (b) 24 (c) 21 (d) 42
  35. 35.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 144 (d) 132
  36. 36.4 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) 8 (b) 12 (c) 16 (d) 6
  37. 37.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
  38. 38.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) 24 (b) 30 (c) 48 (d) 10
  39. 39.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 36 (d) 15
  40. 40.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 55 (c) 66 (d) 110

Answer key

  1. 120
  2. 24
  3. 15
  4. 18
  5. 30
  6. 10
  7. 30
  8. 24
  9. 15
  10. 21
  11. 28
  12. 21
  13. 55
  14. 15
  15. 42
  16. 120
  17. 120
  18. 6
  19. 10
  20. 10
  21. 6
  22. 21
  23. 6
  24. 12
  25. 105
  26. 132
  27. 24
  28. 78
  29. 28
  30. 14
  31. 91
  32. 55
  33. 36
  34. 21
  35. 66
  36. 8
  37. 20
  38. 24
  39. 15
  40. 55

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