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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 369 · 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.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 10 (c) 32 (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) 100 (b) 90 (c) 20 (d) 45
  3. 3.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) 9 (b) 5 (c) 6 (d) 12
  4. 4.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 81 (d) 36
  5. 5.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 78 (d) 91
  6. 6.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
  7. 7.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  8. 8.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 13 (c) 42 (d) 84
  9. 9.6 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) 24 (b) 10 (c) 48 (d) 30
  10. 10.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) 28 (d) 21
  11. 11.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) 21 (b) 10 (c) 42 (d) 24
  12. 12.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
  13. 13.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  14. 14.6 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
  15. 15.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  16. 16.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  17. 17.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  18. 18.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
  19. 19.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 105 (c) 210 (d) 225
  20. 20.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 91 (c) 78 (d) 156
  21. 21.6 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) 36 (b) 30 (c) 11 (d) 60
  22. 22.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 121 (d) 55
  23. 23.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) 18 (b) 9 (c) 12 (d) 6
  24. 24.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 22 (c) 110 (d) 55
  25. 25.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 72 (d) 81
  26. 26.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  27. 27.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  28. 28.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 105 (d) 225
  29. 29.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 15 (c) 21 (d) 36
  30. 30.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 144 (d) 24
  31. 31.5 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) 70 (b) 12 (c) 40 (d) 35
  32. 32.3 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) 9 (b) 21 (c) 36 (d) 18
  33. 33.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) 28 (b) 21 (c) 42 (d) 10
  34. 34.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  35. 35.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  36. 36.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  37. 37.6 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) 42 (c) 12 (d) 36
  38. 38.7 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
  39. 39.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  40. 40.There are 7 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) 56 (b) 35 (c) 11 (d) 28

Answer key

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

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