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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 124 · 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. 1.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 45 (c) 55 (d) 90
  2. 2.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 42 (c) 28 (d) 49
  3. 3.5 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) 40 (b) 25 (c) 20 (d) 9
  4. 4.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  5. 5.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
  6. 6.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 20 (d) 10
  7. 7.6 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) 48 (b) 84 (c) 42 (d) 13
  8. 8.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  9. 9.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 210 (d) 105
  10. 10.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) 24 (c) 8 (d) 18
  11. 11.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  12. 12.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) 13 (b) 84 (c) 48 (d) 42
  13. 13.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 49 (d) 42
  14. 14.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 144 (d) 66
  15. 15.6 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) 12 (b) 36 (c) 72 (d) 42
  16. 16.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 56 (d) 28
  17. 17.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 36 (c) 72 (d) 81
  18. 18.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 182 (d) 196
  19. 19.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 64 (c) 56 (d) 16
  20. 20.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 156 (c) 78 (d) 169
  21. 21.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  22. 22.3 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) 9 (b) 6 (c) 18 (d) 12
  23. 23.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) 35 (b) 60 (c) 30 (d) 11
  24. 24.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  25. 25.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  26. 26.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) 35 (b) 11 (c) 30 (d) 60
  27. 27.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  28. 28.4 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) 32 (b) 56 (c) 28 (d) 11
  29. 29.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 169 (c) 156 (d) 78
  30. 30.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 15 (d) 12
  31. 31.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 55 (c) 66 (d) 121
  32. 32.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 144 (c) 24 (d) 132
  33. 33.There are 3 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) 7 (b) 24 (c) 12 (d) 15
  34. 34.There are 6 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) 42 (b) 36 (c) 12 (d) 72
  35. 35.14 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
  36. 36.3 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) 42 (b) 24 (c) 21 (d) 10
  37. 37.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  38. 38.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) 49 (b) 56 (c) 14 (d) 98
  39. 39.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  40. 40.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) 6 (c) 12 (d) 16

Answer key

  1. 45
  2. 21
  3. 20
  4. 120
  5. 56
  6. 10
  7. 42
  8. 120
  9. 105
  10. 12
  11. 120
  12. 42
  13. 42
  14. 66
  15. 36
  16. 28
  17. 36
  18. 91
  19. 28
  20. 78
  21. 6
  22. 9
  23. 30
  24. 24
  25. 24
  26. 30
  27. 24
  28. 28
  29. 78
  30. 15
  31. 55
  32. 132
  33. 12
  34. 36
  35. 91
  36. 21
  37. 120
  38. 49
  39. 6
  40. 8

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