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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 552 · 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. 1.6 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) 36 (b) 9 (c) 24 (d) 18
  2. 2.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 42 (c) 28 (d) 49
  3. 3.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 110 (c) 66 (d) 55
  4. 4.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  5. 5.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  6. 6.There are 3 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) 10 (b) 42 (c) 21 (d) 24
  7. 7.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 10 (c) 21 (d) 28
  8. 8.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 45 (d) 55
  9. 9.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 132 (c) 66 (d) 78
  10. 10.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 45 (d) 90
  11. 11.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) 18 (b) 24 (c) 12 (d) 8
  12. 12.There are 8 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) 64 (b) 32 (c) 40 (d) 12
  13. 13.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  14. 14.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  15. 15.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) 11 (b) 60 (c) 30 (d) 36
  16. 16.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 28 (d) 56
  17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  18. 18.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 55 (c) 110 (d) 121
  19. 19.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 20 (c) 100 (d) 90
  20. 20.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  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) 30 (d) 21
  22. 22.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  23. 23.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 42 (c) 21 (d) 49
  24. 24.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 25 (d) 11
  25. 25.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 64 (c) 32 (d) 40
  26. 26.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 225 (d) 105
  27. 27.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) 24 (c) 36 (d) 18
  28. 28.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 90 (d) 100
  29. 29.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) 7 (b) 24 (c) 15 (d) 12
  30. 30.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) 21 (b) 42 (c) 28 (d) 10
  31. 31.8 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
  32. 32.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 49 (d) 21
  33. 33.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) 24 (b) 15 (c) 7 (d) 12
  34. 34.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 36 (c) 56 (d) 64
  35. 35.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  36. 36.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
  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) 112 (b) 15 (c) 64 (d) 56
  38. 38.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) 6 (b) 12 (c) 9 (d) 5
  39. 39.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 55 (d) 121
  40. 40.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 78 (d) 66

Answer key

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

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