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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 293 · 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) 28 (b) 42 (c) 21 (d) 49
  2. 2.5 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) 10 (c) 15 (d) 7
  3. 3.3 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) 10 (b) 24 (c) 42 (d) 21
  4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  5. 5.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
  6. 6.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 55 (d) 90
  7. 7.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  8. 8.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
  9. 9.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  10. 10.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 81 (c) 45 (d) 72
  11. 11.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 156 (c) 78 (d) 169
  12. 12.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  13. 13.6 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) 9 (b) 18 (c) 36 (d) 24
  14. 14.7 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) 12 (b) 42 (c) 70 (d) 35
  15. 15.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
  16. 16.There are 4 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) 12 (b) 7 (c) 16 (d) 24
  17. 17.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 105 (d) 210
  18. 18.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  19. 19.There are 8 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) 11 (b) 24 (c) 32 (d) 48
  20. 20.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 72 (d) 36
  21. 21.5 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) 25 (b) 50 (c) 10 (d) 30
  22. 22.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 56 (c) 28 (d) 11
  23. 23.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  24. 24.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 56 (d) 16
  25. 25.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
  26. 26.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  27. 27.3 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) 15 (b) 12 (c) 7 (d) 24
  28. 28.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 66 (d) 24
  29. 29.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) 24 (c) 16 (d) 7
  30. 30.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 20 (c) 25 (d) 10
  31. 31.There are 8 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) 32 (b) 16 (c) 10 (d) 24
  32. 32.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 9 (c) 6 (d) 18
  33. 33.7 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) 14 (b) 9 (c) 21 (d) 28
  34. 34.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) 28 (d) 16
  35. 35.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 36 (d) 81
  36. 36.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 169 (c) 91 (d) 156
  37. 37.There are 4 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 28 (b) 48 (c) 24 (d) 10
  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) 110 (c) 55 (d) 22
  39. 39.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 42 (d) 14
  40. 40.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120

Answer key

  1. 21
  2. 10
  3. 21
  4. 6
  5. 21
  6. 45
  7. 24
  8. 20
  9. 6
  10. 36
  11. 78
  12. 120
  13. 18
  14. 35
  15. 55
  16. 12
  17. 105
  18. 24
  19. 24
  20. 36
  21. 25
  22. 28
  23. 24
  24. 28
  25. 30
  26. 120
  27. 12
  28. 132
  29. 12
  30. 10
  31. 16
  32. 9
  33. 14
  34. 56
  35. 36
  36. 78
  37. 24
  38. 110
  39. 42
  40. 120

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