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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 586 · 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.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 42 (d) 21
  2. 2.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 42 (d) 21
  3. 3.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  4. 4.There are 3 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) 42 (b) 24 (c) 10 (d) 21
  5. 5.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 121 (c) 22 (d) 55
  6. 6.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 22 (c) 55 (d) 110
  7. 7.6 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) 11 (c) 36 (d) 60
  8. 8.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  9. 9.3 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) 5 (b) 12 (c) 6 (d) 9
  10. 10.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  11. 11.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 105 (c) 91 (d) 182
  12. 12.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 24 (c) 10 (d) 28
  13. 13.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  14. 14.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 30 (c) 15 (d) 12
  15. 15.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) 20 (b) 40 (c) 25 (d) 9
  16. 16.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  17. 17.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 91 (d) 182
  18. 18.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 66 (c) 132 (d) 24
  19. 19.3 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) 9 (b) 21 (c) 36 (d) 18
  20. 20.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) 9 (b) 21 (c) 28 (d) 14
  21. 21.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 36 (d) 15
  22. 22.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  23. 23.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  24. 24.7 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) 10 (b) 28 (c) 21 (d) 42
  25. 25.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 49 (c) 28 (d) 42
  26. 26.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 28 (c) 16 (d) 56
  27. 27.There are 6 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) 60 (c) 36 (d) 11
  28. 28.8 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) 11 (b) 24 (c) 48 (d) 32
  29. 29.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  30. 30.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 64 (c) 56 (d) 36
  31. 31.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  32. 32.11 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
  33. 33.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 36 (c) 72 (d) 81
  34. 34.7 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) 28 (c) 21 (d) 14
  35. 35.3 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) 42 (c) 24 (d) 10
  36. 36.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 32 (c) 56 (d) 11
  37. 37.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 156 (c) 78 (d) 169
  38. 38.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 20 (d) 45
  39. 39.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 64 (c) 28 (d) 36
  40. 40.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 10 (d) 15

Answer key

  1. 42
  2. 21
  3. 120
  4. 21
  5. 55
  6. 110
  7. 30
  8. 24
  9. 6
  10. 24
  11. 91
  12. 24
  13. 6
  14. 30
  15. 20
  16. 6
  17. 91
  18. 132
  19. 18
  20. 14
  21. 15
  22. 24
  23. 120
  24. 21
  25. 21
  26. 56
  27. 30
  28. 24
  29. 120
  30. 28
  31. 120
  32. 55
  33. 36
  34. 14
  35. 21
  36. 28
  37. 78
  38. 45
  39. 28
  40. 10

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