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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 554 · 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.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 121 (d) 55
  2. 2.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  3. 3.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  4. 4.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) 30 (b) 11 (c) 35 (d) 60
  5. 5.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  6. 6.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 45 (c) 55 (d) 100
  7. 7.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 28 (c) 36 (d) 56
  8. 8.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 10 (c) 21 (d) 20
  9. 9.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) 18 (b) 24 (c) 36 (d) 9
  10. 10.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 15 (d) 30
  11. 11.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  12. 12.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 66 (d) 55
  13. 13.3 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) 12 (b) 18 (c) 9 (d) 6
  14. 14.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) 48 (d) 10
  15. 15.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
  16. 16.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 81 (c) 45 (d) 36
  17. 17.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 169 (c) 78 (d) 156
  18. 18.7 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) 21 (c) 10 (d) 42
  19. 19.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 121 (c) 22 (d) 110
  20. 20.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 45 (c) 100 (d) 20
  21. 21.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) 21 (b) 9 (c) 18 (d) 36
  22. 22.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 30 (d) 15
  23. 23.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 5 (b) 6 (c) 12 (d) 9
  24. 24.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 182 (d) 91
  25. 25.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 78 (d) 132
  26. 26.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 81 (c) 72 (d) 36
  27. 27.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  28. 28.9 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
  29. 29.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 210 (d) 225
  30. 30.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 25 (d) 11
  31. 31.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  32. 32.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 28 (d) 49
  33. 33.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  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) 40 (b) 24 (c) 9 (d) 20
  35. 35.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  36. 36.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 55 (d) 66
  37. 37.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) 21 (d) 42
  38. 38.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 20 (c) 30 (d) 8
  39. 39.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) 18 (c) 12 (d) 8
  40. 40.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) 36 (b) 9 (c) 24 (d) 18

Answer key

  1. 55
  2. 6
  3. 6
  4. 30
  5. 120
  6. 45
  7. 28
  8. 20
  9. 18
  10. 15
  11. 6
  12. 55
  13. 9
  14. 24
  15. 45
  16. 36
  17. 78
  18. 21
  19. 110
  20. 45
  21. 18
  22. 15
  23. 6
  24. 91
  25. 66
  26. 72
  27. 120
  28. 36
  29. 105
  30. 10
  31. 24
  32. 21
  33. 120
  34. 20
  35. 120
  36. 55
  37. 21
  38. 15
  39. 12
  40. 18

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