← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 29 · 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 canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 10 (c) 21 (d) 42
  2. 2.7 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) 13 (b) 49 (c) 84 (d) 42
  3. 3.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 45 (d) 20
  4. 4.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 42 (d) 21
  5. 5.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 12 (d) 30
  6. 6.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) 18 (b) 8 (c) 30 (d) 15
  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. 8.6 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) 30 (b) 60 (c) 36 (d) 11
  9. 9.8 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) 40 (b) 12 (c) 32 (d) 64
  10. 10.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 30 (d) 15
  11. 11.8 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) 15 (c) 112 (d) 64
  12. 12.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 30 (d) 15
  13. 13.7 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) 28 (b) 9 (c) 14 (d) 21
  14. 14.6 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) 48 (b) 13 (c) 42 (d) 84
  15. 15.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) 24 (b) 18 (c) 12 (d) 8
  16. 16.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 20 (c) 21 (d) 10
  17. 17.There are 8 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) 32 (b) 48 (c) 24 (d) 11
  18. 18.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 36 (d) 81
  19. 19.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 196 (c) 105 (d) 182
  20. 20.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
  21. 21.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  22. 22.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 11 (c) 28 (d) 32
  23. 23.5 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) 15 (b) 20 (c) 30 (d) 8
  24. 24.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  25. 25.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 15 (c) 25 (d) 10
  26. 26.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  27. 27.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  28. 28.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) 49 (c) 42 (d) 13
  29. 29.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 32 (c) 11 (d) 48
  30. 30.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 15 (d) 10
  31. 31.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 105 (d) 120
  32. 32.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  33. 33.5 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) 60 (b) 11 (c) 30 (d) 35
  34. 34.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 60 (c) 30 (d) 35
  35. 35.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 66 (c) 121 (d) 55
  36. 36.12 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
  37. 37.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) 10 (b) 30 (c) 24 (d) 48
  38. 38.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  39. 39.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 9 (c) 40 (d) 25
  40. 40.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 72 (d) 36

Answer key

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

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