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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 468 · 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 captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 28 (c) 16 (d) 64
  2. 2.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 36 (c) 81 (d) 72
  3. 3.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 110 (c) 22 (d) 121
  4. 4.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) 18 (b) 36 (c) 9 (d) 24
  5. 5.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 66 (d) 144
  6. 6.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
  7. 7.There are 5 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) 20 (b) 8 (c) 15 (d) 30
  8. 8.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
  9. 9.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  10. 10.5 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) 7 (b) 15 (c) 10 (d) 20
  11. 11.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 10 (d) 20
  12. 12.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 28 (c) 42 (d) 49
  13. 13.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 28 (d) 56
  14. 14.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 81 (c) 36 (d) 45
  15. 15.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 28 (c) 56 (d) 11
  16. 16.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 15 (d) 10
  17. 17.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 56 (c) 64 (d) 16
  18. 18.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) 11 (b) 48 (c) 32 (d) 24
  19. 19.There are 8 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) 13 (b) 80 (c) 48 (d) 40
  20. 20.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 6 (d) 3
  21. 21.7 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) 70 (b) 42 (c) 35 (d) 12
  22. 22.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) 18 (b) 24 (c) 9 (d) 36
  23. 23.4 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) 12 (b) 8 (c) 16 (d) 6
  24. 24.8 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) 40 (b) 32 (c) 12 (d) 64
  25. 25.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) 14 (b) 28 (c) 9 (d) 21
  26. 26.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  27. 27.3 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) 12 (c) 24 (d) 7
  28. 28.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 42 (d) 49
  29. 29.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 15 (c) 12 (d) 36
  30. 30.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 36 (c) 18 (d) 72
  31. 31.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  32. 32.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  33. 33.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 24 (c) 7 (d) 12
  34. 34.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 210 (d) 105
  35. 35.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 48 (c) 30 (d) 24
  36. 36.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  37. 37.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) 10 (b) 15 (c) 7 (d) 20
  38. 38.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  39. 39.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
  40. 40.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 12 (c) 15 (d) 7

Answer key

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

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