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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 103 · 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. 1.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 78 (c) 132 (d) 144
  2. 2.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  3. 3.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 25 (c) 15 (d) 20
  4. 4.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 15 (c) 25 (d) 10
  5. 5.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 55 (c) 45 (d) 100
  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) 24 (d) 20
  7. 7.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
  8. 8.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 24 (d) 66
  9. 9.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 55 (d) 110
  10. 10.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 66 (d) 132
  11. 11.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 11 (d) 20
  12. 12.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 22 (d) 55
  13. 13.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  14. 14.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 156 (d) 91
  15. 15.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 121 (c) 55 (d) 110
  16. 16.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 28 (c) 36 (d) 56
  17. 17.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 9 (c) 28 (d) 14
  18. 18.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  19. 19.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 66 (c) 78 (d) 132
  20. 20.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 6 (d) 3
  21. 21.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  22. 22.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
  23. 23.There are 6 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) 60 (c) 36 (d) 11
  24. 24.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  25. 25.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 56 (c) 112 (d) 64
  26. 26.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 36 (c) 18 (d) 81
  27. 27.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 78 (c) 169 (d) 156
  28. 28.3 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) 5 (b) 12 (c) 6 (d) 9
  29. 29.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 110 (c) 55 (d) 22
  30. 30.3 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) 15 (b) 7 (c) 12 (d) 24
  31. 31.8 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) 24 (b) 16 (c) 32 (d) 10
  32. 32.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  33. 33.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 56 (c) 36 (d) 28
  34. 34.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  35. 35.7 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) 84 (c) 49 (d) 13
  36. 36.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 72 (d) 81
  37. 37.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 15 (c) 30 (d) 36
  38. 38.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  39. 39.6 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) 36 (b) 30 (c) 11 (d) 60
  40. 40.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

Answer key

  1. 66
  2. 24
  3. 10
  4. 10
  5. 45
  6. 20
  7. 21
  8. 66
  9. 55
  10. 132
  11. 10
  12. 55
  13. 6
  14. 78
  15. 55
  16. 28
  17. 14
  18. 120
  19. 66
  20. 6
  21. 24
  22. 20
  23. 30
  24. 24
  25. 56
  26. 36
  27. 78
  28. 6
  29. 110
  30. 12
  31. 16
  32. 120
  33. 28
  34. 24
  35. 42
  36. 72
  37. 15
  38. 120
  39. 30
  40. 28

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