← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 156 · 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 a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 100 (d) 55
  2. 2.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  3. 3.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  4. 4.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 12 (d) 30
  5. 5.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
  6. 6.6 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) 42 (b) 72 (c) 36 (d) 12
  7. 7.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  8. 8.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  9. 9.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  10. 10.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 12 (c) 24 (d) 15
  11. 11.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
  12. 12.3 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) 15 (b) 7 (c) 24 (d) 12
  13. 13.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  14. 14.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
  15. 15.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) 25 (c) 30 (d) 50
  16. 16.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 66 (d) 55
  17. 17.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 66 (d) 78
  18. 18.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 24 (c) 18 (d) 8
  19. 19.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 36 (c) 64 (d) 56
  20. 20.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 105 (c) 196 (d) 91
  21. 21.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 20 (c) 100 (d) 45
  22. 22.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 66 (d) 132
  23. 23.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 132 (c) 24 (d) 66
  24. 24.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) 11 (b) 56 (c) 32 (d) 28
  25. 25.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) 24 (d) 21
  26. 26.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
  27. 27.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 49 (c) 14 (d) 42
  28. 28.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 6 (c) 5 (d) 9
  29. 29.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) 28 (d) 56
  30. 30.4 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) 28 (c) 32 (d) 56
  31. 31.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 121 (c) 110 (d) 66
  32. 32.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  33. 33.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 120 (c) 225 (d) 210
  34. 34.There are 5 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) 40 (b) 12 (c) 70 (d) 35
  35. 35.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 45 (c) 20 (d) 90
  36. 36.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 28 (c) 10 (d) 48
  37. 37.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 91 (c) 156 (d) 169
  38. 38.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 9 (c) 21 (d) 14
  39. 39.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
  40. 40.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 42 (d) 21

Answer key

  1. 45
  2. 24
  3. 120
  4. 15
  5. 10
  6. 36
  7. 6
  8. 24
  9. 120
  10. 12
  11. 30
  12. 12
  13. 120
  14. 72
  15. 25
  16. 55
  17. 66
  18. 12
  19. 28
  20. 91
  21. 90
  22. 132
  23. 66
  24. 28
  25. 21
  26. 20
  27. 42
  28. 6
  29. 56
  30. 28
  31. 55
  32. 120
  33. 105
  34. 35
  35. 45
  36. 24
  37. 78
  38. 14
  39. 18
  40. 21

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