← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 117 · 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. 1.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 45 (c) 72 (d) 81
  2. 2.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 30 (c) 21 (d) 36
  3. 3.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  4. 4.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 90 (d) 100
  5. 5.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 16 (d) 28
  6. 6.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  7. 7.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 12 (c) 24 (d) 8
  8. 8.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 132 (d) 66
  9. 9.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  10. 10.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 144 (d) 66
  11. 11.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 40 (c) 70 (d) 35
  12. 12.4 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) 11 (b) 56 (c) 28 (d) 32
  13. 13.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 55 (d) 110
  14. 14.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 78 (d) 66
  15. 15.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 105 (d) 225
  16. 16.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  17. 17.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  18. 18.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  19. 19.4 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) 7 (b) 24 (c) 16 (d) 12
  20. 20.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 84 (c) 13 (d) 42
  21. 21.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) 48 (c) 30 (d) 24
  22. 22.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 7 (c) 15 (d) 24
  23. 23.3 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) 6 (b) 9 (c) 12 (d) 18
  24. 24.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 121 (c) 110 (d) 55
  25. 25.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 156 (c) 78 (d) 91
  26. 26.5 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) 50 (b) 25 (c) 30 (d) 10
  27. 27.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) 25 (c) 10 (d) 30
  28. 28.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 66 (d) 132
  29. 29.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  30. 30.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 120 (d) 225
  31. 31.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 21 (d) 28
  32. 32.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  33. 33.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 15 (c) 25 (d) 20
  34. 34.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
  35. 35.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) 42 (d) 21
  36. 36.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) 36 (d) 15
  37. 37.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 21 (d) 49
  38. 38.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 105 (c) 196 (d) 91
  39. 39.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 45 (c) 90 (d) 20
  40. 40.7 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) 42 (d) 84

Answer key

  1. 36
  2. 15
  3. 120
  4. 45
  5. 56
  6. 6
  7. 12
  8. 66
  9. 6
  10. 66
  11. 35
  12. 28
  13. 55
  14. 66
  15. 105
  16. 6
  17. 120
  18. 120
  19. 12
  20. 42
  21. 24
  22. 12
  23. 9
  24. 55
  25. 78
  26. 25
  27. 25
  28. 132
  29. 24
  30. 105
  31. 21
  32. 24
  33. 10
  34. 10
  35. 21
  36. 30
  37. 21
  38. 91
  39. 45
  40. 42

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