← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 5 · 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 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) 100 (d) 90
  2. 2.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) 15 (d) 36
  3. 3.There are 7 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) 42 (b) 28 (c) 21 (d) 10
  4. 4.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  5. 5.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 28 (d) 21
  6. 6.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 42 (c) 21 (d) 24
  7. 7.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  8. 8.There are 4 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) 12 (b) 7 (c) 24 (d) 16
  9. 9.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 25 (c) 20 (d) 10
  10. 10.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
  11. 11.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) 10 (b) 28 (c) 24 (d) 48
  12. 12.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  13. 13.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 78 (c) 144 (d) 132
  14. 14.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 100 (c) 55 (d) 90
  15. 15.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
  16. 16.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  17. 17.8 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
  18. 18.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 45 (c) 81 (d) 36
  19. 19.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  20. 20.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 42 (d) 21
  21. 21.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) 40 (b) 80 (c) 48 (d) 13
  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.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  24. 24.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) 18 (d) 15
  25. 25.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 12 (c) 24 (d) 7
  26. 26.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  27. 27.3 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) 6 (c) 5 (d) 12
  28. 28.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 110 (c) 22 (d) 55
  29. 29.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 91 (d) 182
  30. 30.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) 8 (b) 12 (c) 24 (d) 18
  31. 31.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 21 (d) 15
  32. 32.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 25 (c) 20 (d) 10
  33. 33.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  34. 34.There are 3 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) 15 (c) 24 (d) 7
  35. 35.7 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
  36. 36.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  38. 38.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 20 (c) 15 (d) 30
  39. 39.3 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) 36 (b) 21 (c) 18 (d) 9
  40. 40.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 16 (c) 56 (d) 28

Answer key

  1. 90
  2. 30
  3. 21
  4. 120
  5. 21
  6. 21
  7. 24
  8. 12
  9. 10
  10. 72
  11. 24
  12. 24
  13. 66
  14. 45
  15. 45
  16. 24
  17. 28
  18. 36
  19. 6
  20. 42
  21. 40
  22. 36
  23. 120
  24. 15
  25. 12
  26. 24
  27. 6
  28. 110
  29. 91
  30. 12
  31. 15
  32. 20
  33. 6
  34. 12
  35. 21
  36. 6
  37. 120
  38. 15
  39. 18
  40. 56

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