← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 100 · 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, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 21 (c) 42 (d) 49
  2. 2.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 10 (d) 20
  3. 3.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 78 (c) 169 (d) 91
  4. 4.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  5. 5.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 9 (d) 6
  6. 6.4 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) 28 (b) 24 (c) 10 (d) 48
  7. 7.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 10 (d) 20
  8. 8.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 96 (b) 56 (c) 14 (d) 48
  9. 9.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 36 (d) 45
  10. 10.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) 28 (d) 11
  11. 11.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  12. 12.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 78 (d) 66
  13. 13.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  14. 14.4 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) 24 (d) 12
  15. 15.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 12 (d) 30
  16. 16.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 40 (c) 64 (d) 32
  17. 17.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  18. 18.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 56 (c) 28 (d) 64
  19. 19.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
  20. 20.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 121 (d) 110
  21. 21.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 49 (d) 28
  22. 22.8 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) 48 (b) 13 (c) 80 (d) 40
  23. 23.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  24. 24.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 196 (d) 91
  25. 25.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  26. 26.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 81 (c) 72 (d) 36
  27. 27.6 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) 36 (c) 11 (d) 60
  28. 28.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 36 (d) 30
  29. 29.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 42 (c) 21 (d) 14
  30. 30.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 12 (c) 18 (d) 9
  31. 31.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) 11 (b) 32 (c) 24 (d) 48
  32. 32.5 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
  33. 33.7 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) 9 (b) 21 (c) 28 (d) 14
  34. 34.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 144 (d) 66
  35. 35.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 24 (d) 132
  36. 36.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) 10 (b) 28 (c) 24 (d) 48
  37. 37.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  38. 38.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 45 (d) 90
  39. 39.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) 28 (b) 14 (c) 9 (d) 21
  40. 40.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 132 (d) 144

Answer key

  1. 21
  2. 20
  3. 78
  4. 120
  5. 6
  6. 24
  7. 10
  8. 48
  9. 36
  10. 28
  11. 120
  12. 66
  13. 24
  14. 12
  15. 30
  16. 32
  17. 24
  18. 28
  19. 10
  20. 110
  21. 21
  22. 40
  23. 24
  24. 91
  25. 120
  26. 36
  27. 30
  28. 15
  29. 42
  30. 9
  31. 24
  32. 10
  33. 14
  34. 66
  35. 66
  36. 24
  37. 120
  38. 90
  39. 14
  40. 132

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