← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 302 · 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 how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  2. 2.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  3. 3.4 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) 32 (b) 56 (c) 11 (d) 28
  4. 4.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
  5. 5.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 90 (c) 20 (d) 100
  6. 6.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 132 (d) 66
  7. 7.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  8. 8.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 36 (c) 56 (d) 64
  9. 9.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 42 (d) 49
  10. 10.There are 8 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) 16 (c) 32 (d) 10
  11. 11.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 110 (c) 22 (d) 55
  12. 12.There are 4 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) 8 (b) 32 (c) 16 (d) 20
  13. 13.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 20 (c) 100 (d) 90
  14. 14.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 15 (c) 36 (d) 30
  15. 15.7 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) 35 (b) 28 (c) 56 (d) 11
  16. 16.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  17. 17.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 72 (d) 18
  18. 18.15 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
  19. 19.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  20. 20.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
  21. 21.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 64 (c) 36 (d) 56
  22. 22.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 81 (d) 36
  23. 23.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 105 (c) 210 (d) 120
  24. 24.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 28 (d) 49
  25. 25.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  26. 26.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 25 (c) 10 (d) 50
  27. 27.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 32 (c) 20 (d) 8
  28. 28.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  29. 29.3 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) 7 (b) 15 (c) 12 (d) 24
  30. 30.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 35 (c) 42 (d) 70
  31. 31.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 55 (c) 45 (d) 90
  32. 32.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 24 (c) 66 (d) 144
  33. 33.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) 15 (c) 7 (d) 24
  34. 34.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
  35. 35.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 72 (c) 81 (d) 45
  36. 36.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 132 (d) 144
  37. 37.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  38. 38.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  39. 39.8 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) 80 (b) 40 (c) 13 (d) 48
  40. 40.There are 6 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) 42 (b) 12 (c) 36 (d) 72

Answer key

  1. 6
  2. 24
  3. 28
  4. 20
  5. 90
  6. 66
  7. 6
  8. 28
  9. 21
  10. 16
  11. 110
  12. 16
  13. 45
  14. 15
  15. 28
  16. 6
  17. 72
  18. 105
  19. 24
  20. 10
  21. 28
  22. 36
  23. 105
  24. 21
  25. 24
  26. 25
  27. 16
  28. 120
  29. 12
  30. 35
  31. 45
  32. 132
  33. 12
  34. 56
  35. 36
  36. 66
  37. 120
  38. 24
  39. 40
  40. 36

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