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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 48 · 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 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 42 (c) 12 (d) 35
  2. 2.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 81 (c) 18 (d) 72
  3. 3.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 45 (d) 81
  4. 4.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 210 (d) 225
  5. 5.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  6. 6.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) 9 (b) 40 (c) 20 (d) 24
  7. 7.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) 11 (b) 56 (c) 32 (d) 28
  8. 8.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 20 (d) 10
  9. 9.7 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) 14 (b) 98 (c) 56 (d) 49
  10. 10.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 36 (c) 45 (d) 72
  11. 11.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 21 (c) 49 (d) 14
  12. 12.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  13. 13.3 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) 10 (b) 24 (c) 42 (d) 21
  14. 14.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 18 (c) 8 (d) 30
  15. 15.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  16. 16.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 169 (c) 78 (d) 156
  17. 17.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 42 (d) 28
  18. 18.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) 28 (b) 48 (c) 10 (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) 20 (b) 25 (c) 21 (d) 10
  20. 20.4 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) 10 (b) 48 (c) 24 (d) 28
  21. 21.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 91 (d) 105
  22. 22.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 42 (d) 49
  23. 23.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 90 (c) 45 (d) 100
  24. 24.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 132 (d) 66
  25. 25.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  26. 26.There are 5 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) 35 (b) 12 (c) 40 (d) 70
  27. 27.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 66 (c) 55 (d) 121
  28. 28.6 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) 13 (b) 48 (c) 84 (d) 42
  29. 29.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) 21 (b) 14 (c) 28 (d) 9
  30. 30.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) 24 (b) 12 (c) 7 (d) 16
  31. 31.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 56 (d) 16
  32. 32.4 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) 6 (b) 12 (c) 16 (d) 8
  33. 33.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  34. 34.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
  35. 35.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 182 (c) 91 (d) 196
  36. 36.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
  37. 37.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 28 (c) 56 (d) 36
  38. 38.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 120 (d) 105
  39. 39.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 100 (c) 90 (d) 55
  40. 40.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 156 (c) 169 (d) 78

Answer key

  1. 35
  2. 36
  3. 36
  4. 105
  5. 6
  6. 20
  7. 28
  8. 10
  9. 49
  10. 36
  11. 21
  12. 24
  13. 21
  14. 15
  15. 120
  16. 78
  17. 21
  18. 24
  19. 20
  20. 24
  21. 91
  22. 21
  23. 90
  24. 132
  25. 24
  26. 35
  27. 55
  28. 42
  29. 14
  30. 12
  31. 28
  32. 8
  33. 120
  34. 45
  35. 91
  36. 6
  37. 28
  38. 105
  39. 45
  40. 78

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