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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 295 · 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).

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  1. 1.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  2. 2.There are 5 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) 40 (b) 12 (c) 70 (d) 35
  3. 3.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 45 (d) 90
  4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  5. 5.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 45 (d) 20
  6. 6.5 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) 20 (b) 7 (c) 10 (d) 15
  7. 7.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  8. 8.3 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) 24 (b) 7 (c) 12 (d) 15
  9. 9.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  10. 10.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 105 (d) 210
  11. 11.7 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) 28 (b) 9 (c) 21 (d) 14
  12. 12.8 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) 96 (b) 56 (c) 48 (d) 14
  13. 13.There are 6 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) 18 (b) 12 (c) 8 (d) 24
  14. 14.5 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) 10 (c) 25 (d) 30
  15. 15.4 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) 20 (b) 8 (c) 32 (d) 16
  16. 16.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) 42 (c) 84 (d) 13
  17. 17.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) 9 (c) 14 (d) 28
  18. 18.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15
  19. 19.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 49 (d) 42
  20. 20.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
  21. 21.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 55 (d) 121
  22. 22.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 42 (c) 49 (d) 14
  23. 23.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 42 (c) 10 (d) 24
  24. 24.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  25. 25.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 100 (c) 90 (d) 55
  26. 26.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 30 (c) 20 (d) 8
  27. 27.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  28. 28.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 78 (d) 66
  29. 29.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 56 (c) 28 (d) 64
  30. 30.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 156 (c) 78 (d) 91
  31. 31.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 36 (d) 72
  32. 32.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 25 (c) 15 (d) 20
  33. 33.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 81 (c) 36 (d) 72
  34. 34.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 7 (c) 24 (d) 12
  35. 35.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
  36. 36.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 21 (d) 25
  37. 37.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) 28 (d) 64
  38. 38.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
  39. 39.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 196 (c) 182 (d) 105
  40. 40.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20

Answer key

  1. 24
  2. 35
  3. 90
  4. 6
  5. 45
  6. 10
  7. 120
  8. 12
  9. 24
  10. 105
  11. 14
  12. 48
  13. 12
  14. 25
  15. 16
  16. 42
  17. 14
  18. 15
  19. 21
  20. 21
  21. 55
  22. 42
  23. 21
  24. 6
  25. 45
  26. 15
  27. 24
  28. 66
  29. 28
  30. 78
  31. 36
  32. 10
  33. 72
  34. 12
  35. 55
  36. 20
  37. 56
  38. 110
  39. 91
  40. 120

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