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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 224 · 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 SUN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
  2. 2.4 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) 16 (b) 8 (c) 6 (d) 12
  3. 3.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  4. 4.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  5. 5.There are 5 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) 25 (b) 40 (c) 20 (d) 9
  6. 6.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) 42 (c) 21 (d) 10
  7. 7.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 72 (c) 81 (d) 18
  8. 8.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 144 (c) 78 (d) 66
  9. 9.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 120 (d) 225
  10. 10.There are 7 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) 9 (b) 21 (c) 28 (d) 14
  11. 11.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  12. 12.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  13. 13.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 15 (c) 36 (d) 21
  14. 14.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 45 (d) 81
  15. 15.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 12 (d) 36
  16. 16.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  17. 17.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 210 (c) 105 (d) 225
  18. 18.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  19. 19.There are 4 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) 32 (b) 16 (c) 8 (d) 20
  20. 20.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 14 (c) 21 (d) 49
  21. 21.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 81 (c) 36 (d) 72
  22. 22.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
  23. 23.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 49 (d) 21
  24. 24.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 169 (d) 156
  25. 25.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) 42 (c) 21 (d) 10
  26. 26.There are 3 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) 9 (b) 36 (c) 21 (d) 18
  27. 27.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 66 (d) 144
  28. 28.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
  29. 29.There are 6 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) 24 (b) 18 (c) 8 (d) 12
  30. 30.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 10 (d) 15
  31. 31.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  32. 32.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 42 (c) 21 (d) 28
  33. 33.There are 3 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) 12 (b) 5 (c) 9 (d) 6
  34. 34.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  35. 35.5 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) 35 (c) 11 (d) 30
  36. 36.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) 48 (b) 10 (c) 24 (d) 28
  37. 37.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 64 (c) 36 (d) 56
  38. 38.3 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) 9 (b) 5 (c) 12 (d) 6
  39. 39.4 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) 32 (b) 56 (c) 11 (d) 28
  40. 40.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 25 (d) 120

Answer key

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

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