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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 177 · 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 how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  2. 2.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 80 (b) 13 (c) 48 (d) 40
  3. 3.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  4. 4.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 45 (d) 100
  5. 5.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  6. 6.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) 14 (b) 28 (c) 9 (d) 21
  7. 7.3 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) 12 (b) 9 (c) 6 (d) 18
  8. 8.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) 28 (b) 11 (c) 56 (d) 32
  9. 9.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 225 (c) 210 (d) 120
  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) 10 (b) 21 (c) 28 (d) 42
  11. 11.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 15 (d) 30
  12. 12.3 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) 7 (b) 15 (c) 24 (d) 12
  13. 13.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
  14. 14.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 14 (d) 42
  15. 15.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 40 (c) 9 (d) 25
  16. 16.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 132 (c) 78 (d) 144
  17. 17.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  18. 18.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 28 (c) 56 (d) 64
  19. 19.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 21 (c) 14 (d) 49
  20. 20.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 36 (d) 45
  21. 21.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  22. 22.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 121 (d) 55
  23. 23.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  24. 24.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 91 (c) 156 (d) 78
  25. 25.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) 84 (c) 48 (d) 42
  26. 26.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  27. 27.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  28. 28.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  29. 29.8 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) 15 (b) 112 (c) 64 (d) 56
  30. 30.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  31. 31.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  32. 32.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) 21 (c) 42 (d) 24
  33. 33.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 15 (d) 10
  34. 34.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 182 (c) 196 (d) 91
  35. 35.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 55 (d) 66
  36. 36.7 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) 21 (b) 14 (c) 28 (d) 9
  37. 37.There are 8 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) 96 (b) 56 (c) 14 (d) 48
  38. 38.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 132 (c) 78 (d) 66
  39. 39.6 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) 24 (c) 9 (d) 18
  40. 40.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 15 (d) 30

Answer key

  1. 120
  2. 40
  3. 120
  4. 45
  5. 6
  6. 14
  7. 9
  8. 28
  9. 105
  10. 21
  11. 15
  12. 12
  13. 28
  14. 21
  15. 20
  16. 66
  17. 120
  18. 28
  19. 42
  20. 36
  21. 24
  22. 55
  23. 24
  24. 78
  25. 42
  26. 24
  27. 24
  28. 120
  29. 56
  30. 24
  31. 6
  32. 21
  33. 10
  34. 91
  35. 55
  36. 14
  37. 48
  38. 66
  39. 18
  40. 15

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