← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 155 · 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 FISH be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  2. 2.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) 48 (b) 10 (c) 30 (d) 24
  3. 3.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 45 (d) 90
  4. 4.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) 8 (b) 30 (c) 15 (d) 18
  5. 5.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 18 (c) 72 (d) 36
  6. 6.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 91 (d) 196
  7. 7.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 105 (c) 196 (d) 182
  8. 8.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 32 (c) 16 (d) 24
  9. 9.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 32 (c) 64 (d) 12
  10. 10.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 15 (c) 20 (d) 10
  11. 11.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) 21 (b) 24 (c) 42 (d) 10
  12. 12.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 64 (d) 16
  13. 13.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 24 (d) 66
  14. 14.4 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) 40 (b) 20 (c) 9 (d) 24
  15. 15.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) 20 (b) 24 (c) 40 (d) 9
  16. 16.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10
  17. 17.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) 24 (b) 36 (c) 18 (d) 9
  18. 18.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 81 (d) 45
  19. 19.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 66 (d) 78
  20. 20.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 36 (d) 64
  21. 21.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 18 (d) 72
  22. 22.There are 4 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) 28 (b) 32 (c) 11 (d) 56
  23. 23.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 28 (d) 64
  24. 24.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
  25. 25.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  26. 26.There are 3 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 21 (c) 18 (d) 36
  27. 27.3 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) 9 (b) 18 (c) 21 (d) 36
  28. 28.There are 8 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) 48 (b) 11 (c) 32 (d) 24
  29. 29.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 42 (c) 84 (d) 48
  30. 30.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) 36 (c) 18 (d) 9
  31. 31.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 156 (c) 169 (d) 91
  32. 32.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 110 (d) 55
  33. 33.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 24 (d) 132
  34. 34.6 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
  35. 35.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  36. 36.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) 9 (c) 6 (d) 12
  37. 37.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  38. 38.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  39. 39.7 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) 42 (b) 10 (c) 28 (d) 21
  40. 40.There are 7 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) 42 (b) 70 (c) 12 (d) 35

Answer key

  1. 24
  2. 24
  3. 90
  4. 15
  5. 36
  6. 91
  7. 91
  8. 16
  9. 32
  10. 10
  11. 21
  12. 56
  13. 132
  14. 20
  15. 20
  16. 10
  17. 18
  18. 36
  19. 66
  20. 28
  21. 72
  22. 28
  23. 28
  24. 36
  25. 24
  26. 18
  27. 18
  28. 24
  29. 42
  30. 18
  31. 78
  32. 55
  33. 66
  34. 15
  35. 120
  36. 9
  37. 120
  38. 120
  39. 21
  40. 35

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