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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 641 · 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 team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 14 (d) 42
  2. 2.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  3. 3.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 64 (d) 16
  4. 4.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
  5. 5.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 72 (c) 81 (d) 45
  6. 6.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 121 (d) 55
  7. 7.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 225 (c) 120 (d) 105
  8. 8.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 56 (c) 16 (d) 64
  9. 9.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 36 (d) 30
  10. 10.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 30 (d) 12
  11. 11.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 66 (d) 121
  12. 12.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) 12 (b) 16 (c) 8 (d) 6
  13. 13.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  14. 14.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 15 (d) 10
  15. 15.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 15 (d) 10
  16. 16.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 132 (c) 66 (d) 144
  17. 17.13 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
  18. 18.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  19. 19.5 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) 35 (b) 12 (c) 40 (d) 70
  20. 20.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  21. 21.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  22. 22.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 66 (d) 144
  23. 23.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 144 (c) 66 (d) 132
  24. 24.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 20 (d) 45
  25. 25.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 121 (d) 55
  26. 26.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  27. 27.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 30 (c) 15 (d) 21
  28. 28.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 55 (c) 90 (d) 45
  29. 29.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 56 (c) 36 (d) 28
  30. 30.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 55 (c) 121 (d) 110
  31. 31.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  32. 32.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 10 (c) 20 (d) 21
  33. 33.7 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) 28 (b) 11 (c) 35 (d) 56
  34. 34.There are 5 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) 40 (b) 25 (c) 9 (d) 20
  35. 35.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 64 (c) 28 (d) 56
  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) 10 (b) 24 (c) 21 (d) 42
  37. 37.There are 7 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) 84 (b) 42 (c) 13 (d) 49
  38. 38.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  39. 39.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 91 (d) 105
  40. 40.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) 10 (b) 16 (c) 32 (d) 24

Answer key

  1. 21
  2. 6
  3. 56
  4. 90
  5. 36
  6. 55
  7. 105
  8. 28
  9. 30
  10. 15
  11. 55
  12. 8
  13. 6
  14. 10
  15. 10
  16. 132
  17. 78
  18. 120
  19. 35
  20. 24
  21. 24
  22. 66
  23. 66
  24. 45
  25. 55
  26. 120
  27. 15
  28. 45
  29. 28
  30. 110
  31. 24
  32. 20
  33. 28
  34. 20
  35. 28
  36. 21
  37. 42
  38. 120
  39. 91
  40. 16

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