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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 476 · 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 SUN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  2. 2.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  3. 3.3 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) 21 (b) 10 (c) 24 (d) 42
  4. 4.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 110 (c) 55 (d) 22
  5. 5.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 36 (d) 18
  6. 6.7 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) 12 (d) 70
  7. 7.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 20 (d) 90
  8. 8.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 49 (d) 21
  9. 9.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 100 (c) 55 (d) 90
  10. 10.5 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) 30 (d) 25
  11. 11.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 42 (d) 28
  12. 12.4 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) 11 (b) 28 (c) 56 (d) 32
  13. 13.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  14. 14.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 49 (d) 28
  15. 15.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  16. 16.8 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) 48 (b) 32 (c) 11 (d) 24
  17. 17.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) 42 (b) 24 (c) 21 (d) 10
  18. 18.5 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) 60 (b) 11 (c) 35 (d) 30
  19. 19.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 45 (c) 81 (d) 36
  20. 20.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 182 (c) 196 (d) 91
  21. 21.3 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) 30 (b) 8 (c) 15 (d) 18
  22. 22.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) 144 (d) 132
  23. 23.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 10 (c) 15 (d) 20
  24. 24.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 110 (d) 55
  25. 25.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 21 (c) 36 (d) 30
  26. 26.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 18 (c) 21 (d) 9
  27. 27.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 121 (d) 66
  28. 28.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 210 (c) 225 (d) 120
  29. 29.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 100 (d) 45
  30. 30.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 30 (d) 12
  31. 31.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 90 (d) 100
  32. 32.7 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) 21 (b) 28 (c) 14 (d) 9
  33. 33.There are 7 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) 42 (b) 28 (c) 21 (d) 10
  34. 34.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  35. 35.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 20 (d) 10
  36. 36.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 96 (c) 48 (d) 14
  37. 37.There are 6 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) 48 (b) 13 (c) 84 (d) 42
  38. 38.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
  39. 39.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 210 (c) 120 (d) 105
  40. 40.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6

Answer key

  1. 6
  2. 24
  3. 21
  4. 110
  5. 36
  6. 35
  7. 90
  8. 21
  9. 45
  10. 25
  11. 21
  12. 28
  13. 24
  14. 21
  15. 24
  16. 24
  17. 21
  18. 30
  19. 36
  20. 91
  21. 15
  22. 132
  23. 10
  24. 55
  25. 15
  26. 18
  27. 55
  28. 105
  29. 45
  30. 15
  31. 45
  32. 14
  33. 21
  34. 120
  35. 10
  36. 48
  37. 42
  38. 66
  39. 105
  40. 6

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