← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 14 · 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. 1.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 210 (c) 225 (d) 120
  2. 2.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) 9 (b) 28 (c) 21 (d) 14
  3. 3.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 16 (c) 64 (d) 56
  4. 4.7 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) 70 (b) 42 (c) 35 (d) 12
  5. 5.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 45 (c) 20 (d) 100
  6. 6.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
  7. 7.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
  8. 8.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 10 (c) 15 (d) 20
  9. 9.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  10. 10.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  11. 11.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 20 (d) 10
  12. 12.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 112 (b) 15 (c) 56 (d) 64
  13. 13.4 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) 8 (b) 20 (c) 32 (d) 16
  14. 14.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  15. 15.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) 10 (b) 21 (c) 42 (d) 24
  16. 16.6 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) 9 (b) 24 (c) 36 (d) 18
  17. 17.7 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) 98 (b) 56 (c) 14 (d) 49
  18. 18.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 120 (c) 210 (d) 225
  19. 19.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 15 (d) 12
  20. 20.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 81 (d) 45
  21. 21.3 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) 10 (b) 42 (c) 24 (d) 21
  22. 22.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 66 (d) 144
  23. 23.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
  24. 24.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 21 (d) 49
  25. 25.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 42 (d) 49
  26. 26.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) 18 (b) 8 (c) 12 (d) 24
  27. 27.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 64 (c) 16 (d) 56
  28. 28.7 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) 11 (b) 35 (c) 56 (d) 28
  29. 29.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 48 (c) 80 (d) 40
  30. 30.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) 30 (b) 48 (c) 10 (d) 24
  31. 31.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 55 (d) 22
  32. 32.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 18 (d) 36
  33. 33.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  34. 34.8 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) 14 (b) 96 (c) 56 (d) 48
  35. 35.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  36. 36.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  37. 37.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 36 (c) 24 (d) 18
  38. 38.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 121 (d) 66
  39. 39.There are 4 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) 32 (b) 20 (c) 16 (d) 8
  40. 40.There are 3 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) 6 (b) 18 (c) 12 (d) 9

Answer key

  1. 105
  2. 14
  3. 28
  4. 35
  5. 45
  6. 42
  7. 45
  8. 10
  9. 6
  10. 24
  11. 10
  12. 56
  13. 16
  14. 120
  15. 21
  16. 18
  17. 49
  18. 105
  19. 30
  20. 36
  21. 21
  22. 66
  23. 90
  24. 21
  25. 42
  26. 12
  27. 56
  28. 28
  29. 40
  30. 24
  31. 55
  32. 36
  33. 24
  34. 48
  35. 24
  36. 120
  37. 18
  38. 55
  39. 16
  40. 9

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