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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 751 · 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. 1.4 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) 16 (b) 32 (c) 20 (d) 8
  2. 2.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 42 (d) 49
  3. 3.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  4. 4.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 132 (c) 66 (d) 78
  5. 5.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  6. 6.3 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) 15 (c) 7 (d) 12
  7. 7.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  8. 8.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 64 (c) 56 (d) 16
  9. 9.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  10. 10.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 49 (d) 42
  11. 11.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 169 (d) 91
  12. 12.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 15 (d) 20
  13. 13.7 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) 56 (c) 11 (d) 28
  14. 14.There are 7 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) 49 (b) 84 (c) 13 (d) 42
  15. 15.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 15 (c) 36 (d) 12
  16. 16.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 132 (d) 144
  17. 17.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
  18. 18.3 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) 18 (b) 36 (c) 9 (d) 21
  19. 19.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  20. 20.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) 28 (c) 24 (d) 10
  21. 21.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 66 (c) 78 (d) 132
  22. 22.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  23. 23.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
  24. 24.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 45 (c) 100 (d) 20
  25. 25.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  26. 26.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  27. 27.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 105 (d) 225
  28. 28.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 12 (c) 15 (d) 36
  29. 29.There are 7 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) 49 (b) 56 (c) 14 (d) 98
  30. 30.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) 32 (b) 11 (c) 56 (d) 28
  31. 31.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
  32. 32.5 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) 30 (c) 25 (d) 10
  33. 33.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 30 (c) 35 (d) 11
  34. 34.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 66 (c) 55 (d) 110
  35. 35.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 64 (c) 36 (d) 28
  36. 36.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) 30 (b) 48 (c) 10 (d) 24
  37. 37.There are 3 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) 18 (b) 15 (c) 30 (d) 8
  38. 38.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  39. 39.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) 40 (b) 9 (c) 20 (d) 25
  40. 40.There are 5 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) 30 (b) 60 (c) 35 (d) 11

Answer key

  1. 16
  2. 21
  3. 24
  4. 66
  5. 24
  6. 12
  7. 6
  8. 56
  9. 6
  10. 21
  11. 78
  12. 10
  13. 28
  14. 42
  15. 15
  16. 66
  17. 28
  18. 18
  19. 120
  20. 24
  21. 66
  22. 120
  23. 36
  24. 45
  25. 24
  26. 24
  27. 105
  28. 30
  29. 49
  30. 28
  31. 42
  32. 25
  33. 30
  34. 55
  35. 28
  36. 24
  37. 15
  38. 120
  39. 20
  40. 30

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