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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 542 · 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 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 10 (d) 11
  2. 2.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 15 (c) 10 (d) 25
  3. 3.14 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
  4. 4.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 21 (d) 28
  5. 5.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 18 (d) 36
  6. 6.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 15 (c) 21 (d) 30
  7. 7.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 45 (d) 100
  8. 8.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) 50 (b) 30 (c) 10 (d) 25
  9. 9.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  10. 10.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 15 (d) 25
  11. 11.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 90 (c) 100 (d) 55
  12. 12.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 20 (d) 10
  13. 13.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 15 (d) 30
  14. 14.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
  15. 15.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  16. 16.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 78 (c) 91 (d) 169
  17. 17.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 110 (d) 55
  18. 18.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 28 (c) 64 (d) 36
  19. 19.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  20. 20.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  21. 21.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  22. 22.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  23. 23.5 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) 11 (b) 30 (c) 60 (d) 35
  24. 24.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) 20 (b) 7 (c) 10 (d) 15
  25. 25.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  26. 26.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
  27. 27.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 36 (d) 81
  28. 28.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 6 (c) 18 (d) 12
  29. 29.There are 4 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) 32 (b) 28 (c) 11 (d) 56
  30. 30.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 66 (d) 132
  31. 31.8 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) 80 (b) 13 (c) 48 (d) 40
  32. 32.5 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) 12 (b) 35 (c) 70 (d) 40
  33. 33.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
  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) 9 (b) 20 (c) 40 (d) 25
  35. 35.7 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) 14 (b) 9 (c) 21 (d) 28
  36. 36.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 132 (d) 144
  37. 37.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  38. 38.6 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) 12 (c) 72 (d) 36
  39. 39.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) 24 (b) 15 (c) 7 (d) 12
  40. 40.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 66 (d) 55

Answer key

  1. 10
  2. 10
  3. 91
  4. 21
  5. 36
  6. 15
  7. 45
  8. 25
  9. 120
  10. 10
  11. 45
  12. 20
  13. 15
  14. 14
  15. 24
  16. 78
  17. 55
  18. 28
  19. 6
  20. 6
  21. 24
  22. 120
  23. 30
  24. 10
  25. 120
  26. 105
  27. 72
  28. 9
  29. 28
  30. 66
  31. 40
  32. 35
  33. 15
  34. 20
  35. 14
  36. 66
  37. 24
  38. 36
  39. 12
  40. 55

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