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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 31 · 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).

NameDateTime takenScore ___ / 40
  1. 1.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 28 (d) 49
  2. 2.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  3. 3.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  4. 4.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 196 (c) 105 (d) 182
  5. 5.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 81 (c) 18 (d) 72
  6. 6.5 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) 25 (b) 20 (c) 9 (d) 40
  7. 7.7 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) 49 (c) 98 (d) 14
  8. 8.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 132 (d) 66
  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) 20 (c) 21 (d) 10
  10. 10.3 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) 9 (c) 12 (d) 6
  11. 11.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  12. 12.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 12 (c) 35 (d) 40
  13. 13.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 30 (d) 15
  14. 14.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 64 (d) 36
  15. 15.5 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) 70 (b) 35 (c) 12 (d) 40
  16. 16.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  17. 17.There are 6 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) 24 (b) 36 (c) 18 (d) 9
  18. 18.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
  19. 19.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  20. 20.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 15 (d) 25
  21. 21.6 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
  22. 22.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  23. 23.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  24. 24.There are 6 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) 12 (b) 18 (c) 24 (d) 8
  25. 25.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 28 (d) 64
  26. 26.4 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) 24 (b) 20 (c) 9 (d) 40
  27. 27.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 16 (c) 56 (d) 64
  28. 28.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 121 (c) 22 (d) 110
  29. 29.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 28 (d) 21
  30. 30.There are 3 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) 18 (b) 21 (c) 36 (d) 9
  31. 31.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 91 (d) 156
  32. 32.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  33. 33.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 15 (d) 36
  34. 34.There are 8 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) 24 (b) 32 (c) 16 (d) 10
  35. 35.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  36. 36.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 36 (c) 56 (d) 64
  37. 37.8 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) 16 (b) 32 (c) 10 (d) 24
  38. 38.There are 6 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) 10 (b) 48 (c) 24 (d) 30
  39. 39.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 14 (c) 21 (d) 42
  40. 40.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) 12 (b) 24 (c) 7 (d) 15

Answer key

  1. 21
  2. 6
  3. 6
  4. 91
  5. 72
  6. 20
  7. 49
  8. 132
  9. 20
  10. 6
  11. 24
  12. 35
  13. 15
  14. 28
  15. 35
  16. 120
  17. 18
  18. 45
  19. 24
  20. 10
  21. 15
  22. 120
  23. 120
  24. 12
  25. 28
  26. 20
  27. 56
  28. 110
  29. 21
  30. 18
  31. 78
  32. 6
  33. 15
  34. 16
  35. 24
  36. 28
  37. 16
  38. 24
  39. 21
  40. 12

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