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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 119 · 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.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 55 (d) 66
  2. 2.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 56 (d) 28
  3. 3.4 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) 8 (b) 16 (c) 12 (d) 6
  4. 4.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 14 (c) 98 (d) 49
  5. 5.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) 12 (c) 24 (d) 15
  6. 6.There are 5 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) 15 (b) 7 (c) 10 (d) 20
  7. 7.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 12 (d) 15
  8. 8.7 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) 35 (b) 11 (c) 56 (d) 28
  9. 9.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) 24 (b) 10 (c) 32 (d) 16
  10. 10.5 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) 7 (b) 15 (c) 10 (d) 20
  11. 11.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 15 (d) 20
  12. 12.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 55 (d) 100
  13. 13.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  14. 14.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 91 (d) 182
  15. 15.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 28 (d) 21
  16. 16.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 45 (d) 81
  17. 17.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  18. 18.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) 36 (b) 72 (c) 12 (d) 42
  19. 19.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 100 (d) 90
  20. 20.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 105 (d) 210
  21. 21.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  22. 22.8 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) 10 (b) 32 (c) 24 (d) 16
  23. 23.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) 40 (c) 64 (d) 32
  24. 24.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  25. 25.There are 5 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 50 (c) 30 (d) 25
  26. 26.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 21 (c) 15 (d) 36
  27. 27.4 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) 28 (b) 10 (c) 24 (d) 48
  28. 28.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 91 (d) 156
  29. 29.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 12 (d) 30
  30. 30.There are 3 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 8 (c) 18 (d) 15
  31. 31.6 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) 18 (b) 8 (c) 24 (d) 12
  32. 32.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  33. 33.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) 40 (b) 12 (c) 70 (d) 35
  34. 34.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  35. 35.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  36. 36.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  37. 37.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  38. 38.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) 12 (b) 35 (c) 70 (d) 42
  39. 39.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 156 (c) 91 (d) 169
  40. 40.3 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) 12 (b) 6 (c) 18 (d) 9

Answer key

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

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