← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 259 · 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 a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 10 (d) 20
  2. 2.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  3. 3.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 45 (c) 90 (d) 100
  4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  5. 5.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 91 (c) 182 (d) 105
  6. 6.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 56 (d) 28
  7. 7.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 30 (c) 36 (d) 15
  8. 8.There are 8 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) 112 (b) 56 (c) 15 (d) 64
  9. 9.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 49 (b) 98 (c) 14 (d) 56
  10. 10.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 81 (d) 36
  11. 11.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  12. 12.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
  13. 13.There are 6 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) 24 (b) 12 (c) 18 (d) 8
  14. 14.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  15. 15.6 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) 24 (b) 12 (c) 8 (d) 18
  16. 16.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 66 (d) 144
  17. 17.There are 5 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) 30 (b) 8 (c) 15 (d) 20
  18. 18.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  19. 19.There are 8 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) 40 (c) 64 (d) 32
  20. 20.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
  21. 21.8 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
  22. 22.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 36 (c) 15 (d) 21
  23. 23.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 28 (d) 64
  24. 24.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  25. 25.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 56 (c) 36 (d) 64
  26. 26.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 100 (c) 55 (d) 45
  27. 27.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 36 (d) 15
  28. 28.5 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) 35 (b) 11 (c) 30 (d) 60
  29. 29.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 45 (d) 36
  30. 30.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 28 (d) 49
  31. 31.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 55 (c) 110 (d) 66
  32. 32.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  33. 33.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) 25 (d) 21
  34. 34.There are 4 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) 16 (d) 8
  35. 35.6 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) 12 (b) 42 (c) 72 (d) 36
  36. 36.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 144 (c) 66 (d) 78
  37. 37.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  38. 38.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 36 (c) 81 (d) 72
  39. 39.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 49 (d) 42
  40. 40.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) 28 (b) 32 (c) 56 (d) 11

Answer key

  1. 10
  2. 120
  3. 90
  4. 6
  5. 91
  6. 56
  7. 30
  8. 56
  9. 49
  10. 36
  11. 120
  12. 55
  13. 12
  14. 120
  15. 12
  16. 66
  17. 15
  18. 24
  19. 32
  20. 15
  21. 28
  22. 15
  23. 28
  24. 24
  25. 28
  26. 45
  27. 15
  28. 30
  29. 36
  30. 21
  31. 55
  32. 120
  33. 20
  34. 8
  35. 36
  36. 66
  37. 24
  38. 36
  39. 21
  40. 28

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad