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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 404 · 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 team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 14 (d) 42
  2. 2.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  3. 3.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 21 (d) 49
  4. 4.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 55 (c) 90 (d) 45
  5. 5.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 121 (d) 55
  6. 6.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 121 (c) 55 (d) 110
  7. 7.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  8. 8.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) 60 (b) 30 (c) 35 (d) 11
  9. 9.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) 30 (d) 15
  10. 10.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) 21 (d) 42
  11. 11.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 66 (d) 55
  12. 12.5 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) 15 (d) 10
  13. 13.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 144 (c) 66 (d) 78
  14. 14.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 64 (c) 36 (d) 28
  15. 15.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 66 (d) 132
  16. 16.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  17. 17.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 78 (d) 91
  18. 18.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) 24 (b) 18 (c) 8 (d) 12
  19. 19.6 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) 30 (c) 10 (d) 48
  20. 20.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) 13 (b) 40 (c) 48 (d) 80
  21. 21.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  22. 22.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) 8 (b) 24 (c) 12 (d) 18
  23. 23.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 20 (c) 32 (d) 16
  24. 24.There are 7 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) 10 (b) 28 (c) 42 (d) 21
  25. 25.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 210 (c) 225 (d) 105
  26. 26.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  27. 27.9 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
  28. 28.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  29. 29.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 16 (c) 24 (d) 10
  30. 30.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 45 (c) 90 (d) 55
  31. 31.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  32. 32.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 110 (c) 121 (d) 22
  33. 33.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 45 (c) 100 (d) 20
  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) 12 (d) 24
  35. 35.4 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) 7 (b) 24 (c) 12 (d) 16
  36. 36.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 105 (c) 196 (d) 182
  37. 37.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 15 (d) 30
  38. 38.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
  39. 39.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  40. 40.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 30 (d) 12

Answer key

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

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