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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 445 · 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.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  2. 2.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
  3. 3.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 55 (d) 110
  4. 4.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 40 (c) 24 (d) 20
  5. 5.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 100 (d) 45
  6. 6.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 11 (c) 30 (d) 60
  7. 7.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 14 (b) 98 (c) 49 (d) 56
  8. 8.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  9. 9.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 10 (c) 15 (d) 20
  10. 10.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  11. 11.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) 8 (b) 30 (c) 15 (d) 18
  12. 12.7 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) 9 (b) 28 (c) 21 (d) 14
  13. 13.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 28 (d) 21
  14. 14.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 24 (d) 132
  15. 15.4 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) 10 (b) 48 (c) 28 (d) 24
  16. 16.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 21 (d) 14
  17. 17.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 210 (c) 120 (d) 225
  18. 18.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 20 (d) 25
  19. 19.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 45 (c) 90 (d) 100
  20. 20.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
  21. 21.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) 36 (b) 24 (c) 18 (d) 9
  22. 22.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  23. 23.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 9 (d) 6
  24. 24.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 18 (d) 36
  25. 25.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  26. 26.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 49 (c) 42 (d) 14
  27. 27.6 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) 42 (b) 84 (c) 13 (d) 48
  28. 28.8 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
  29. 29.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  30. 30.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  31. 31.There are 7 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) 10 (b) 42 (c) 21 (d) 28
  32. 32.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 42 (c) 21 (d) 28
  33. 33.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 182 (d) 105
  34. 34.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 5 (c) 6 (d) 9
  35. 35.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 132 (d) 144
  36. 36.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 66 (d) 144
  37. 37.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  38. 38.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 56 (c) 16 (d) 28
  39. 39.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 55 (c) 110 (d) 22
  40. 40.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) 56 (c) 11 (d) 28

Answer key

  1. 24
  2. 90
  3. 55
  4. 20
  5. 45
  6. 30
  7. 49
  8. 24
  9. 10
  10. 24
  11. 15
  12. 14
  13. 21
  14. 66
  15. 24
  16. 21
  17. 105
  18. 20
  19. 45
  20. 28
  21. 18
  22. 120
  23. 6
  24. 36
  25. 6
  26. 42
  27. 42
  28. 28
  29. 120
  30. 6
  31. 21
  32. 21
  33. 91
  34. 6
  35. 66
  36. 66
  37. 24
  38. 56
  39. 110
  40. 28

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