← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 539 · 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) 121 (b) 55 (c) 110 (d) 22
  2. 2.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
  3. 3.8 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) 56 (b) 112 (c) 15 (d) 64
  4. 4.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  5. 5.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 49 (d) 21
  6. 6.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 196 (c) 182 (d) 105
  7. 7.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  8. 8.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 15 (d) 36
  9. 9.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) 9 (b) 12 (c) 6 (d) 18
  10. 10.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 55 (d) 66
  11. 11.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 36 (c) 72 (d) 81
  12. 12.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  13. 13.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 81 (c) 36 (d) 72
  14. 14.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) 35 (c) 70 (d) 12
  15. 15.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 45 (c) 36 (d) 81
  16. 16.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) 56 (b) 49 (c) 98 (d) 14
  17. 17.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  18. 18.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  19. 19.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 132 (c) 144 (d) 66
  20. 20.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  21. 21.4 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) 16 (b) 32 (c) 20 (d) 8
  22. 22.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) 24 (c) 10 (d) 30
  23. 23.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 225 (c) 105 (d) 120
  24. 24.There are 5 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) 11 (b) 60 (c) 35 (d) 30
  25. 25.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
  26. 26.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) 14 (b) 9 (c) 21 (d) 28
  27. 27.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  28. 28.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 15 (d) 10
  29. 29.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
  30. 30.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  31. 31.5 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) 11 (b) 30 (c) 35 (d) 60
  32. 32.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 90 (d) 100
  33. 33.3 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) 6 (b) 12 (c) 18 (d) 9
  34. 34.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 42 (d) 49
  35. 35.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
  36. 36.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 60 (c) 36 (d) 30
  37. 37.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 55 (d) 121
  38. 38.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 28 (c) 10 (d) 21
  39. 39.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) 24 (b) 30 (c) 48 (d) 10
  40. 40.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 16 (c) 48 (d) 12

Answer key

  1. 55
  2. 15
  3. 56
  4. 24
  5. 21
  6. 91
  7. 24
  8. 15
  9. 9
  10. 55
  11. 36
  12. 24
  13. 36
  14. 35
  15. 36
  16. 49
  17. 120
  18. 24
  19. 132
  20. 120
  21. 16
  22. 24
  23. 105
  24. 30
  25. 30
  26. 14
  27. 120
  28. 10
  29. 72
  30. 120
  31. 30
  32. 90
  33. 9
  34. 21
  35. 66
  36. 30
  37. 110
  38. 21
  39. 24
  40. 24

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