← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 230 · 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 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 28 (d) 64
  2. 2.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 121 (c) 110 (d) 66
  3. 3.7 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) 9 (c) 28 (d) 14
  4. 4.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) 98 (b) 56 (c) 49 (d) 14
  5. 5.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) 9 (b) 21 (c) 18 (d) 36
  6. 6.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  7. 7.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 12 (c) 8 (d) 16
  8. 8.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  9. 9.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 100 (d) 90
  10. 10.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 12 (c) 15 (d) 36
  11. 11.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 20 (d) 25
  12. 12.8 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) 13 (b) 80 (c) 40 (d) 48
  13. 13.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 10 (c) 24 (d) 30
  14. 14.4 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) 56 (c) 32 (d) 28
  15. 15.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 21 (c) 14 (d) 49
  16. 16.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 6 (d) 3
  17. 17.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 21 (d) 15
  18. 18.There are 5 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) 15 (b) 20 (c) 7 (d) 10
  19. 19.5 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) 40 (b) 70 (c) 35 (d) 12
  20. 20.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 12 (c) 36 (d) 30
  21. 21.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
  22. 22.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 40 (c) 80 (d) 13
  23. 23.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 100 (d) 45
  24. 24.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) 49 (b) 84 (c) 13 (d) 42
  25. 25.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  26. 26.8 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) 112 (b) 64 (c) 15 (d) 56
  27. 27.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 28 (d) 56
  28. 28.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 36 (c) 18 (d) 81
  29. 29.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 25 (d) 15
  30. 30.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 132 (d) 144
  31. 31.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 156 (d) 78
  32. 32.There are 7 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) 14 (c) 21 (d) 28
  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) 18 (c) 81 (d) 72
  34. 34.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 81 (c) 72 (d) 36
  35. 35.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 14 (d) 42
  36. 36.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 121 (d) 55
  37. 37.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 64 (c) 36 (d) 28
  38. 38.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 105 (d) 120
  39. 39.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 156 (d) 169
  40. 40.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 50 (c) 25 (d) 30

Answer key

  1. 28
  2. 55
  3. 14
  4. 49
  5. 18
  6. 120
  7. 8
  8. 120
  9. 45
  10. 30
  11. 20
  12. 40
  13. 24
  14. 28
  15. 42
  16. 6
  17. 15
  18. 10
  19. 35
  20. 15
  21. 110
  22. 40
  23. 45
  24. 42
  25. 6
  26. 56
  27. 28
  28. 36
  29. 10
  30. 66
  31. 78
  32. 14
  33. 72
  34. 36
  35. 21
  36. 55
  37. 28
  38. 105
  39. 78
  40. 25

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