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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 40 · 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 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 30 (c) 50 (d) 25
  2. 2.6 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 30 (b) 11 (c) 60 (d) 36
  3. 3.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  4. 4.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) 28 (b) 9 (c) 14 (d) 21
  5. 5.5 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) 15 (b) 20 (c) 8 (d) 30
  6. 6.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 225 (c) 210 (d) 120
  7. 7.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 36 (c) 81 (d) 72
  8. 8.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 18 (d) 36
  9. 9.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 36 (d) 72
  10. 10.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 64 (d) 28
  11. 11.7 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) 28 (b) 21 (c) 14 (d) 9
  12. 12.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 15 (c) 20 (d) 25
  13. 13.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
  14. 14.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  15. 15.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 25 (d) 10
  16. 16.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 20 (d) 25
  17. 17.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  18. 18.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  19. 19.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 144 (c) 132 (d) 78
  20. 20.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 55 (c) 110 (d) 66
  21. 21.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 225 (d) 210
  22. 22.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 100 (c) 45 (d) 90
  23. 23.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 66 (c) 78 (d) 144
  24. 24.3 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) 36 (b) 9 (c) 18 (d) 21
  25. 25.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  26. 26.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 12 (d) 15
  27. 27.4 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) 12 (b) 6 (c) 8 (d) 16
  28. 28.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 90 (c) 100 (d) 45
  29. 29.6 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) 42 (b) 72 (c) 12 (d) 36
  30. 30.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 10 (d) 20
  31. 31.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
  32. 32.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  33. 33.6 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) 10 (b) 48 (c) 30 (d) 24
  34. 34.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) 7 (b) 24 (c) 12 (d) 16
  35. 35.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) 42 (c) 84 (d) 48
  36. 36.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 32 (c) 24 (d) 11
  37. 37.8 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) 64 (b) 40 (c) 12 (d) 32
  38. 38.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  39. 39.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 72 (d) 36
  40. 40.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 132 (c) 144 (d) 24

Answer key

  1. 25
  2. 30
  3. 6
  4. 14
  5. 15
  6. 105
  7. 72
  8. 36
  9. 36
  10. 28
  11. 14
  12. 10
  13. 90
  14. 24
  15. 10
  16. 20
  17. 24
  18. 24
  19. 66
  20. 55
  21. 105
  22. 45
  23. 66
  24. 18
  25. 120
  26. 15
  27. 8
  28. 45
  29. 36
  30. 10
  31. 6
  32. 120
  33. 24
  34. 12
  35. 42
  36. 24
  37. 32
  38. 24
  39. 36
  40. 132

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