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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 455 · 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.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  2. 2.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  3. 3.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 42 (c) 84 (d) 49
  4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  5. 5.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 42 (d) 21
  6. 6.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  7. 7.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 81 (c) 36 (d) 72
  8. 8.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 169 (c) 156 (d) 91
  9. 9.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  10. 10.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) 18 (b) 8 (c) 15 (d) 30
  11. 11.8 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) 80 (b) 48 (c) 40 (d) 13
  12. 12.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  13. 13.5 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) 30 (c) 35 (d) 11
  14. 14.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
  15. 15.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 66 (d) 55
  16. 16.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 25 (d) 10
  17. 17.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  18. 18.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 15 (d) 10
  19. 19.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 15 (d) 30
  20. 20.7 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) 11 (b) 56 (c) 35 (d) 28
  21. 21.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) 24 (b) 36 (c) 9 (d) 18
  22. 22.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  23. 23.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
  24. 24.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 56 (d) 28
  25. 25.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
  26. 26.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 105 (d) 210
  27. 27.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  28. 28.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 36 (d) 81
  29. 29.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 105 (c) 91 (d) 196
  30. 30.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  31. 31.6 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
  32. 32.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 16 (c) 28 (d) 64
  33. 33.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 81 (c) 72 (d) 18
  34. 34.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 20 (c) 24 (d) 40
  35. 35.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  36. 36.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 56 (c) 32 (d) 28
  37. 37.7 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) 56 (b) 49 (c) 14 (d) 98
  38. 38.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
  39. 39.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 12 (c) 9 (d) 6
  40. 40.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) 10 (b) 28 (c) 42 (d) 21

Answer key

  1. 6
  2. 24
  3. 42
  4. 6
  5. 21
  6. 24
  7. 36
  8. 78
  9. 120
  10. 15
  11. 40
  12. 6
  13. 30
  14. 110
  15. 55
  16. 10
  17. 120
  18. 10
  19. 15
  20. 28
  21. 18
  22. 120
  23. 66
  24. 28
  25. 28
  26. 105
  27. 120
  28. 36
  29. 91
  30. 24
  31. 15
  32. 56
  33. 72
  34. 20
  35. 24
  36. 28
  37. 49
  38. 21
  39. 9
  40. 21

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