← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 137 · 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 MATHS be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  2. 2.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 28 (c) 56 (d) 64
  3. 3.There are 7 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) 13 (b) 49 (c) 42 (d) 84
  4. 4.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) 6 (b) 12 (c) 18 (d) 9
  5. 5.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) 56 (b) 14 (c) 49 (d) 98
  6. 6.There are 4 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) 48 (b) 28 (c) 24 (d) 10
  7. 7.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  8. 8.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 30 (d) 36
  9. 9.There are 7 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) 14 (b) 56 (c) 49 (d) 98
  10. 10.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  11. 11.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
  12. 12.There are 5 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) 10 (b) 50 (c) 25 (d) 30
  13. 13.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) 84 (b) 13 (c) 42 (d) 49
  14. 14.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 24 (d) 66
  15. 15.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 14 (c) 21 (d) 42
  16. 16.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 91 (c) 196 (d) 105
  17. 17.7 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) 9 (b) 21 (c) 14 (d) 28
  18. 18.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 49 (d) 21
  19. 19.5 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) 25 (b) 9 (c) 40 (d) 20
  20. 20.3 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) 24 (b) 10 (c) 42 (d) 21
  21. 21.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  22. 22.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 72 (d) 81
  23. 23.6 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) 36 (d) 72
  24. 24.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 55 (d) 121
  25. 25.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 15 (d) 36
  26. 26.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 91 (d) 78
  27. 27.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) 9 (b) 36 (c) 24 (d) 18
  28. 28.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  29. 29.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 45 (c) 100 (d) 90
  30. 30.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 144 (c) 132 (d) 66
  31. 31.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 48 (c) 96 (d) 14
  32. 32.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) 50 (b) 30 (c) 10 (d) 25
  33. 33.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 20 (d) 25
  34. 34.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 132 (d) 144
  35. 35.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 55 (d) 110
  36. 36.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 28 (d) 64
  37. 37.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 55 (c) 100 (d) 45
  38. 38.7 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
  39. 39.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 225 (d) 120
  40. 40.8 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) 32 (c) 10 (d) 16

Answer key

  1. 120
  2. 28
  3. 42
  4. 9
  5. 49
  6. 24
  7. 24
  8. 30
  9. 49
  10. 24
  11. 28
  12. 25
  13. 42
  14. 66
  15. 21
  16. 91
  17. 14
  18. 21
  19. 20
  20. 21
  21. 6
  22. 36
  23. 36
  24. 110
  25. 15
  26. 78
  27. 18
  28. 120
  29. 45
  30. 66
  31. 48
  32. 25
  33. 20
  34. 132
  35. 55
  36. 56
  37. 45
  38. 21
  39. 105
  40. 16

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