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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 57 · 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).

NameDateTime takenScore ___ / 40
  1. 1.3 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) 6 (b) 12 (c) 5 (d) 9
  2. 2.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  3. 3.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 78 (d) 66
  4. 4.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  5. 5.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) 15 (c) 7 (d) 24
  6. 6.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
  7. 7.There are 3 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) 24 (b) 10 (c) 42 (d) 21
  8. 8.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  9. 9.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 169 (c) 91 (d) 156
  10. 10.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  11. 11.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 36 (c) 81 (d) 72
  12. 12.3 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) 21 (c) 24 (d) 10
  13. 13.5 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) 10 (b) 50 (c) 25 (d) 30
  14. 14.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
  15. 15.3 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) 15 (b) 24 (c) 7 (d) 12
  16. 16.5 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) 12 (b) 70 (c) 35 (d) 40
  17. 17.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) 12 (d) 6
  18. 18.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
  19. 19.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) 21 (d) 25
  20. 20.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
  21. 21.4 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) 6 (b) 12 (c) 8 (d) 16
  22. 22.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 15 (c) 30 (d) 36
  23. 23.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 20 (d) 11
  24. 24.4 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) 40 (b) 20 (c) 24 (d) 9
  25. 25.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  26. 26.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 91 (c) 78 (d) 156
  27. 27.4 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) 24 (b) 7 (c) 12 (d) 16
  28. 28.There are 5 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) 40 (b) 70 (c) 35 (d) 12
  29. 29.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 110 (c) 55 (d) 121
  30. 30.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 110 (d) 121
  31. 31.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) 56 (b) 14 (c) 96 (d) 48
  32. 32.There are 8 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) 10 (b) 24 (c) 32 (d) 16
  33. 33.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 15 (c) 21 (d) 36
  34. 34.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 10 (c) 21 (d) 28
  35. 35.4 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) 11 (c) 56 (d) 28
  36. 36.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 72 (c) 18 (d) 36
  37. 37.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 22 (d) 110
  38. 38.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  39. 39.7 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) 42 (b) 35 (c) 70 (d) 12
  40. 40.5 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) 15 (b) 8 (c) 20 (d) 30

Answer key

  1. 6
  2. 6
  3. 66
  4. 120
  5. 12
  6. 6
  7. 21
  8. 24
  9. 78
  10. 120
  11. 36
  12. 21
  13. 25
  14. 66
  15. 12
  16. 35
  17. 6
  18. 24
  19. 20
  20. 9
  21. 8
  22. 15
  23. 10
  24. 20
  25. 6
  26. 78
  27. 12
  28. 35
  29. 55
  30. 110
  31. 48
  32. 16
  33. 15
  34. 21
  35. 28
  36. 72
  37. 55
  38. 120
  39. 35
  40. 15

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