← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 993 · 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.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) 30 (b) 25 (c) 10 (d) 50
  2. 2.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
  3. 3.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 20 (d) 15
  4. 4.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  5. 5.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 45 (d) 55
  6. 6.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 210 (c) 105 (d) 120
  7. 7.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  8. 8.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) 56 (b) 98 (c) 49 (d) 14
  9. 9.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
  10. 10.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  11. 11.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  12. 12.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  13. 13.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 10 (d) 11
  14. 14.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 98 (b) 14 (c) 49 (d) 56
  15. 15.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) 35 (d) 30
  16. 16.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
  17. 17.7 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) 21 (b) 42 (c) 28 (d) 10
  18. 18.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
  19. 19.There are 5 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) 40 (b) 20 (c) 9 (d) 25
  20. 20.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 66 (c) 121 (d) 110
  21. 21.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  22. 22.4 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) 16 (b) 7 (c) 12 (d) 24
  23. 23.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  24. 24.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 132 (d) 144
  25. 25.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 36 (c) 72 (d) 81
  26. 26.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) 21 (d) 42
  27. 27.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 110 (c) 22 (d) 121
  28. 28.5 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) 20 (b) 15 (c) 8 (d) 30
  29. 29.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) 14 (b) 9 (c) 28 (d) 21
  30. 30.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 15 (c) 36 (d) 12
  31. 31.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 21 (d) 49
  32. 32.4 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) 20 (b) 9 (c) 24 (d) 40
  33. 33.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 91 (d) 78
  34. 34.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 49 (d) 42
  35. 35.6 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) 8 (b) 24 (c) 12 (d) 18
  36. 36.8 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) 48 (b) 56 (c) 14 (d) 96
  37. 37.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 182 (c) 91 (d) 105
  38. 38.There are 7 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) 11 (b) 28 (c) 35 (d) 56
  39. 39.6 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) 18 (b) 9 (c) 36 (d) 24
  40. 40.3 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) 21 (b) 24 (c) 10 (d) 42

Answer key

  1. 25
  2. 56
  3. 10
  4. 24
  5. 45
  6. 105
  7. 24
  8. 49
  9. 30
  10. 120
  11. 120
  12. 24
  13. 10
  14. 49
  15. 30
  16. 6
  17. 21
  18. 18
  19. 20
  20. 55
  21. 6
  22. 12
  23. 6
  24. 66
  25. 36
  26. 42
  27. 110
  28. 15
  29. 14
  30. 15
  31. 21
  32. 20
  33. 78
  34. 21
  35. 12
  36. 48
  37. 91
  38. 28
  39. 18
  40. 21

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