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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 540 · 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 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 45 (d) 100
  2. 2.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
  3. 3.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 100 (c) 55 (d) 45
  4. 4.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  5. 5.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 12 (d) 30
  6. 6.8 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) 40 (b) 80 (c) 13 (d) 48
  7. 7.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 72 (c) 81 (d) 18
  8. 8.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 144 (d) 132
  9. 9.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
  10. 10.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 121 (c) 110 (d) 66
  11. 11.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 169 (d) 78
  12. 12.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  13. 13.There are 4 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) 20 (b) 16 (c) 8 (d) 32
  14. 14.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 64 (c) 28 (d) 16
  15. 15.There are 8 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) 48 (b) 11 (c) 32 (d) 24
  16. 16.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 132 (d) 66
  17. 17.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  18. 18.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
  19. 19.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 21 (d) 49
  20. 20.There are 4 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) 10 (b) 28 (c) 24 (d) 48
  21. 21.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 105 (c) 91 (d) 182
  22. 22.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 91 (d) 105
  23. 23.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 132 (d) 144
  24. 24.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 105 (c) 225 (d) 210
  25. 25.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 9 (c) 36 (d) 18
  26. 26.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 15 (c) 36 (d) 21
  27. 27.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  28. 28.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 10 (c) 15 (d) 20
  29. 29.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 20 (c) 100 (d) 45
  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) 24 (c) 12 (d) 7
  31. 31.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  32. 32.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  33. 33.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 14 (c) 49 (d) 42
  34. 34.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 81 (c) 18 (d) 72
  35. 35.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
  36. 36.6 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) 24 (d) 30
  37. 37.8 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) 56 (b) 112 (c) 64 (d) 15
  38. 38.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 66 (c) 132 (d) 24
  39. 39.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 28 (c) 56 (d) 64
  40. 40.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 9 (d) 12

Answer key

  1. 45
  2. 55
  3. 45
  4. 120
  5. 30
  6. 40
  7. 72
  8. 66
  9. 20
  10. 55
  11. 78
  12. 120
  13. 16
  14. 28
  15. 24
  16. 66
  17. 24
  18. 36
  19. 21
  20. 24
  21. 91
  22. 91
  23. 66
  24. 105
  25. 18
  26. 15
  27. 6
  28. 10
  29. 90
  30. 12
  31. 24
  32. 120
  33. 21
  34. 36
  35. 10
  36. 24
  37. 56
  38. 132
  39. 28
  40. 6

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