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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 15 · 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 a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 21 (d) 49
  2. 2.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  3. 3.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 36 (c) 81 (d) 72
  4. 4.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 132 (d) 66
  5. 5.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 49 (c) 21 (d) 14
  6. 6.6 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) 48 (b) 13 (c) 84 (d) 42
  7. 7.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  8. 8.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  9. 9.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 55 (c) 110 (d) 121
  10. 10.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 132 (c) 144 (d) 24
  11. 11.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 100 (d) 90
  12. 12.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  13. 13.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) 22 (d) 110
  14. 14.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 12 (c) 8 (d) 6
  15. 15.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  16. 16.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  17. 17.There are 6 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) 13 (b) 42 (c) 48 (d) 84
  18. 18.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 30 (c) 36 (d) 21
  19. 19.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 20 (c) 30 (d) 8
  20. 20.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) 21 (b) 9 (c) 28 (d) 14
  21. 21.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 49 (d) 42
  22. 22.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 55 (d) 100
  23. 23.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 81 (d) 36
  24. 24.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 21 (d) 25
  25. 25.8 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) 64 (b) 32 (c) 40 (d) 12
  26. 26.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 21 (c) 42 (d) 10
  27. 27.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) 48 (b) 30 (c) 10 (d) 24
  28. 28.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  29. 29.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  30. 30.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
  31. 31.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 11 (d) 20
  32. 32.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
  33. 33.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 36 (c) 72 (d) 18
  34. 34.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 11 (c) 24 (d) 48
  35. 35.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  36. 36.12 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
  37. 37.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
  38. 38.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 100 (c) 20 (d) 45
  39. 39.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 49 (d) 42
  40. 40.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 36 (d) 15

Answer key

  1. 21
  2. 120
  3. 36
  4. 66
  5. 42
  6. 42
  7. 6
  8. 6
  9. 55
  10. 132
  11. 45
  12. 24
  13. 110
  14. 8
  15. 120
  16. 120
  17. 42
  18. 15
  19. 15
  20. 14
  21. 21
  22. 45
  23. 36
  24. 20
  25. 32
  26. 21
  27. 24
  28. 120
  29. 120
  30. 32
  31. 10
  32. 55
  33. 36
  34. 24
  35. 24
  36. 66
  37. 21
  38. 90
  39. 21
  40. 15

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