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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 3 · 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 5 players. In how many ways can this be done? (a) 21 (b) 25 (c) 10 (d) 20
  2. 2.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  3. 3.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 21 (c) 28 (d) 42
  4. 4.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  5. 5.There are 8 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) 64 (b) 15 (c) 56 (d) 112
  6. 6.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
  7. 7.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  8. 8.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 72 (b) 12 (c) 42 (d) 36
  9. 9.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 28 (d) 49
  10. 10.There are 6 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) 11 (b) 60 (c) 36 (d) 30
  11. 11.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 14 (d) 21
  12. 12.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 56 (c) 28 (d) 36
  13. 13.4 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) 16 (c) 8 (d) 6
  14. 14.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 20 (c) 10 (d) 25
  15. 15.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 42 (c) 14 (d) 21
  16. 16.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  17. 17.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  18. 18.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 10 (d) 25
  19. 19.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  20. 20.4 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) 11 (b) 32 (c) 28 (d) 56
  21. 21.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  22. 22.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 9 (c) 18 (d) 21
  23. 23.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 45 (c) 55 (d) 90
  24. 24.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 182 (d) 91
  25. 25.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 32 (c) 20 (d) 16
  26. 26.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 21 (b) 28 (c) 10 (d) 42
  27. 27.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 48 (d) 16
  28. 28.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 36 (d) 18
  29. 29.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) 48 (b) 24 (c) 30 (d) 10
  30. 30.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 12 (d) 15
  31. 31.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  32. 32.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 30 (c) 36 (d) 21
  33. 33.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 132 (d) 66
  34. 34.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 156 (d) 78
  35. 35.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  36. 36.5 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) 20 (d) 10
  37. 37.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) 9 (b) 36 (c) 18 (d) 24
  38. 38.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 22 (c) 110 (d) 55
  39. 39.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
  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. 20
  2. 120
  3. 21
  4. 24
  5. 56
  6. 78
  7. 24
  8. 36
  9. 21
  10. 30
  11. 21
  12. 28
  13. 8
  14. 10
  15. 42
  16. 24
  17. 6
  18. 10
  19. 6
  20. 28
  21. 6
  22. 18
  23. 45
  24. 91
  25. 16
  26. 21
  27. 24
  28. 36
  29. 24
  30. 15
  31. 120
  32. 15
  33. 132
  34. 78
  35. 24
  36. 10
  37. 18
  38. 110
  39. 45
  40. 12

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