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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 77 · 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 canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 12 (c) 16 (d) 6
  2. 2.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 100 (c) 55 (d) 45
  3. 3.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 121 (c) 110 (d) 66
  4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  5. 5.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) 11 (d) 56
  6. 6.3 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) 6 (b) 12 (c) 9 (d) 18
  7. 7.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  8. 8.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 210 (c) 105 (d) 225
  9. 9.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) 16 (d) 56
  10. 10.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  11. 11.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 45 (c) 81 (d) 36
  12. 12.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 78 (c) 91 (d) 156
  13. 13.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 30 (d) 21
  14. 14.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 45 (c) 20 (d) 90
  15. 15.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  16. 16.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 84 (b) 13 (c) 48 (d) 42
  17. 17.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  18. 18.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) 18 (d) 12
  19. 19.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) 16 (b) 7 (c) 24 (d) 12
  20. 20.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 24 (d) 144
  21. 21.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  22. 22.6 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
  23. 23.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  24. 24.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 15 (d) 36
  25. 25.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55
  26. 26.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 28 (d) 42
  27. 27.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 49 (d) 21
  28. 28.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 42 (c) 21 (d) 49
  29. 29.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  30. 30.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 64 (c) 36 (d) 28
  31. 31.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  32. 32.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 15 (c) 25 (d) 20
  33. 33.5 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) 70 (b) 40 (c) 35 (d) 12
  34. 34.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 10 (c) 25 (d) 20
  35. 35.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
  36. 36.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 64 (d) 28
  37. 37.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  38. 38.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 132 (c) 78 (d) 66
  39. 39.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
  40. 40.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 72 (b) 36 (c) 42 (d) 12

Answer key

  1. 8
  2. 45
  3. 55
  4. 6
  5. 28
  6. 9
  7. 6
  8. 105
  9. 56
  10. 120
  11. 36
  12. 78
  13. 15
  14. 90
  15. 6
  16. 42
  17. 120
  18. 12
  19. 12
  20. 66
  21. 120
  22. 12
  23. 24
  24. 15
  25. 55
  26. 21
  27. 21
  28. 42
  29. 24
  30. 28
  31. 120
  32. 10
  33. 35
  34. 10
  35. 24
  36. 28
  37. 24
  38. 66
  39. 36
  40. 36

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