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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 685 · 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. 1.5 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) 20 (b) 7 (c) 15 (d) 10
  2. 2.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 105 (c) 120 (d) 210
  3. 3.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55
  4. 4.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 14 (c) 42 (d) 21
  5. 5.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) 12 (b) 7 (c) 15 (d) 24
  6. 6.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  7. 7.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 36 (d) 64
  8. 8.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  9. 9.6 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) 72 (b) 12 (c) 36 (d) 42
  10. 10.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 91 (c) 105 (d) 196
  11. 11.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 45 (c) 20 (d) 90
  12. 12.6 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
  13. 13.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 84 (b) 49 (c) 13 (d) 42
  14. 14.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 20 (c) 100 (d) 45
  15. 15.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 55 (c) 121 (d) 110
  16. 16.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 90 (c) 45 (d) 100
  17. 17.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 35 (c) 30 (d) 60
  18. 18.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 21 (c) 15 (d) 36
  19. 19.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) 12 (b) 16 (c) 24 (d) 7
  20. 20.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
  21. 21.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 15 (c) 10 (d) 25
  22. 22.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 18 (d) 72
  23. 23.5 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) 30 (b) 20 (c) 8 (d) 15
  24. 24.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 91 (c) 78 (d) 169
  25. 25.6 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) 11 (b) 30 (c) 60 (d) 36
  26. 26.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  27. 27.6 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) 24 (b) 9 (c) 18 (d) 36
  28. 28.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  29. 29.5 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) 60 (b) 30 (c) 11 (d) 35
  30. 30.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  31. 31.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  32. 32.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 21 (c) 10 (d) 25
  33. 33.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 49 (c) 42 (d) 21
  34. 34.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 18 (c) 72 (d) 36
  35. 35.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) 18 (b) 21 (c) 9 (d) 36
  36. 36.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 28 (d) 21
  37. 37.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 132 (d) 66
  38. 38.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 16 (c) 28 (d) 64
  39. 39.4 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) 6 (b) 8 (c) 16 (d) 12
  40. 40.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 121 (d) 110

Answer key

  1. 10
  2. 105
  3. 55
  4. 21
  5. 12
  6. 120
  7. 28
  8. 24
  9. 36
  10. 91
  11. 45
  12. 15
  13. 42
  14. 90
  15. 55
  16. 45
  17. 30
  18. 15
  19. 12
  20. 42
  21. 10
  22. 72
  23. 15
  24. 78
  25. 30
  26. 24
  27. 18
  28. 120
  29. 30
  30. 6
  31. 120
  32. 20
  33. 21
  34. 36
  35. 18
  36. 21
  37. 66
  38. 56
  39. 8
  40. 110

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