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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 47 · 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) 32 (b) 20 (c) 8 (d) 16
  2. 2.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 64 (b) 112 (c) 15 (d) 56
  3. 3.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  4. 4.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  5. 5.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  6. 6.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 144 (c) 132 (d) 78
  7. 7.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 12 (d) 30
  8. 8.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 55 (c) 66 (d) 110
  9. 9.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 10 (c) 15 (d) 20
  10. 10.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 14 (d) 42
  11. 11.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
  12. 12.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  13. 13.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) 20 (b) 30 (c) 15 (d) 8
  14. 14.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  15. 15.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 105 (d) 91
  16. 16.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
  17. 17.There are 8 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) 96 (b) 56 (c) 14 (d) 48
  18. 18.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  19. 19.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 25 (d) 20
  20. 20.4 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) 12 (b) 6 (c) 8 (d) 16
  21. 21.There are 8 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) 80 (b) 13 (c) 40 (d) 48
  22. 22.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  23. 23.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) 24 (b) 7 (c) 16 (d) 12
  24. 24.5 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
  25. 25.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 10 (d) 25
  26. 26.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) 14 (b) 28 (c) 21 (d) 9
  27. 27.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  28. 28.6 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) 24 (b) 18 (c) 8 (d) 12
  29. 29.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 28 (d) 56
  30. 30.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) 12 (b) 8 (c) 24 (d) 18
  31. 31.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 6 (c) 8 (d) 12
  32. 32.There are 4 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 7 (b) 16 (c) 24 (d) 12
  33. 33.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 91 (d) 105
  34. 34.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 66 (d) 132
  35. 35.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 98 (b) 56 (c) 49 (d) 14
  36. 36.There are 8 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 24 (c) 11 (d) 32
  37. 37.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 66 (c) 78 (d) 144
  38. 38.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) 30 (b) 35 (c) 60 (d) 11
  39. 39.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 18 (c) 36 (d) 81
  40. 40.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 12 (c) 9 (d) 18

Answer key

  1. 16
  2. 56
  3. 120
  4. 24
  5. 24
  6. 66
  7. 15
  8. 55
  9. 10
  10. 21
  11. 36
  12. 120
  13. 15
  14. 120
  15. 91
  16. 6
  17. 48
  18. 24
  19. 20
  20. 8
  21. 40
  22. 120
  23. 12
  24. 25
  25. 10
  26. 14
  27. 120
  28. 12
  29. 56
  30. 12
  31. 8
  32. 12
  33. 91
  34. 66
  35. 49
  36. 24
  37. 66
  38. 30
  39. 72
  40. 9

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