← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 44 · 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. 1.7 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) 21 (b) 14 (c) 9 (d) 28
  2. 2.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  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) 28 (b) 21 (c) 42 (d) 10
  4. 4.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) 48 (b) 28 (c) 10 (d) 24
  5. 5.5 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) 9 (b) 25 (c) 40 (d) 20
  6. 6.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) 49 (b) 56 (c) 14 (d) 98
  7. 7.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 49 (d) 42
  8. 8.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 14 (d) 42
  9. 9.4 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) 24 (b) 40 (c) 9 (d) 20
  10. 10.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 11 (d) 10
  11. 11.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) 84 (c) 42 (d) 49
  12. 12.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 56 (c) 11 (d) 28
  13. 13.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 132 (d) 144
  14. 14.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 81 (c) 18 (d) 36
  15. 15.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 15 (c) 10 (d) 20
  16. 16.3 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) 12 (b) 9 (c) 5 (d) 6
  17. 17.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 210 (c) 225 (d) 105
  18. 18.There are 5 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) 50 (b) 30 (c) 10 (d) 25
  19. 19.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  20. 20.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 3 (d) 12
  21. 21.There are 4 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) 20 (b) 9 (c) 24 (d) 40
  22. 22.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  23. 23.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
  24. 24.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  25. 25.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  26. 26.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 15 (d) 30
  27. 27.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) 21 (b) 42 (c) 10 (d) 24
  28. 28.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
  29. 29.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  30. 30.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) 28 (b) 32 (c) 56 (d) 11
  31. 31.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  32. 32.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 64 (d) 28
  33. 33.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 15 (d) 10
  34. 34.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 169 (c) 156 (d) 91
  35. 35.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  36. 36.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) 21 (b) 28 (c) 14 (d) 9
  37. 37.6 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) 12 (b) 24 (c) 18 (d) 8
  38. 38.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  39. 39.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 36 (d) 45
  40. 40.8 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) 11 (b) 32 (c) 48 (d) 24

Answer key

  1. 14
  2. 6
  3. 21
  4. 24
  5. 20
  6. 49
  7. 21
  8. 42
  9. 20
  10. 10
  11. 42
  12. 28
  13. 66
  14. 72
  15. 10
  16. 6
  17. 105
  18. 25
  19. 120
  20. 6
  21. 20
  22. 24
  23. 55
  24. 120
  25. 24
  26. 15
  27. 21
  28. 45
  29. 24
  30. 28
  31. 24
  32. 56
  33. 10
  34. 78
  35. 6
  36. 14
  37. 12
  38. 120
  39. 36
  40. 24

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