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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 196 · 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.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) 10 (b) 42 (c) 28 (d) 21
  2. 2.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 90 (c) 100 (d) 45
  3. 3.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
  4. 4.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 42 (d) 49
  5. 5.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 144 (d) 132
  6. 6.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  7. 7.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 56 (d) 28
  8. 8.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  9. 9.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  10. 10.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 18 (c) 36 (d) 72
  11. 11.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  12. 12.7 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) 42 (b) 12 (c) 35 (d) 70
  13. 13.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 66 (d) 144
  14. 14.There are 7 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) 14 (b) 98 (c) 49 (d) 56
  15. 15.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  16. 16.5 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) 30 (b) 25 (c) 50 (d) 10
  17. 17.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 36 (d) 72
  18. 18.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 30 (d) 15
  19. 19.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 91 (c) 78 (d) 169
  20. 20.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  21. 21.7 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) 42 (b) 21 (c) 28 (d) 10
  22. 22.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 55 (c) 90 (d) 100
  23. 23.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) 84 (b) 13 (c) 48 (d) 42
  24. 24.5 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) 12 (b) 40 (c) 70 (d) 35
  25. 25.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 182 (d) 196
  26. 26.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 20 (d) 10
  27. 27.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  28. 28.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 15 (d) 20
  29. 29.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
  30. 30.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 20 (d) 10
  31. 31.7 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) 14 (b) 49 (c) 56 (d) 98
  32. 32.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 10 (c) 48 (d) 28
  33. 33.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 28 (c) 56 (d) 36
  34. 34.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 45 (c) 90 (d) 100
  35. 35.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 132 (d) 144
  36. 36.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  37. 37.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 20 (c) 16 (d) 8
  38. 38.6 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) 48 (b) 13 (c) 42 (d) 84
  39. 39.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 18 (c) 15 (d) 30
  40. 40.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 40 (c) 80 (d) 48

Answer key

  1. 21
  2. 45
  3. 21
  4. 21
  5. 66
  6. 24
  7. 28
  8. 24
  9. 24
  10. 36
  11. 6
  12. 35
  13. 66
  14. 49
  15. 6
  16. 25
  17. 36
  18. 30
  19. 78
  20. 6
  21. 21
  22. 45
  23. 42
  24. 35
  25. 91
  26. 10
  27. 120
  28. 10
  29. 15
  30. 20
  31. 49
  32. 24
  33. 28
  34. 90
  35. 66
  36. 120
  37. 16
  38. 42
  39. 15
  40. 40

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