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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 84 · 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 11 players. In how many ways can this be done? (a) 121 (b) 55 (c) 110 (d) 22
  2. 2.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 16 (c) 64 (d) 56
  3. 3.3 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) 9 (c) 6 (d) 12
  4. 4.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 55 (c) 121 (d) 110
  5. 5.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 78 (c) 144 (d) 132
  6. 6.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 20 (c) 25 (d) 10
  7. 7.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  8. 8.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
  9. 9.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  10. 10.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  11. 11.8 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
  12. 12.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  13. 13.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 72 (d) 36
  14. 14.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 105 (d) 225
  15. 15.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  16. 16.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  17. 17.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 24 (c) 9 (d) 20
  18. 18.There are 8 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) 64 (b) 32 (c) 40 (d) 12
  19. 19.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 18 (c) 72 (d) 81
  20. 20.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  21. 21.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  22. 22.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  23. 23.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) 98 (b) 14 (c) 56 (d) 49
  24. 24.There are 6 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) 9 (b) 36 (c) 18 (d) 24
  25. 25.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 55 (c) 90 (d) 100
  26. 26.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 80 (b) 40 (c) 48 (d) 13
  27. 27.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) 11 (c) 35 (d) 30
  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) 8 (c) 18 (d) 12
  29. 29.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 105 (c) 182 (d) 196
  30. 30.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) 56 (d) 16
  31. 31.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) 21 (c) 10 (d) 24
  32. 32.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
  33. 33.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
  34. 34.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 32 (c) 64 (d) 40
  35. 35.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 30 (c) 48 (d) 10
  36. 36.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) 18 (b) 24 (c) 8 (d) 12
  37. 37.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  38. 38.7 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) 56 (b) 98 (c) 14 (d) 49
  39. 39.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
  40. 40.11 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

Answer key

  1. 110
  2. 28
  3. 6
  4. 55
  5. 66
  6. 10
  7. 120
  8. 42
  9. 6
  10. 120
  11. 28
  12. 120
  13. 36
  14. 105
  15. 24
  16. 24
  17. 20
  18. 32
  19. 36
  20. 6
  21. 120
  22. 120
  23. 49
  24. 18
  25. 45
  26. 40
  27. 30
  28. 12
  29. 91
  30. 56
  31. 21
  32. 66
  33. 30
  34. 32
  35. 24
  36. 12
  37. 6
  38. 49
  39. 20
  40. 55

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