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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 642 · 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).

NameDateTime takenScore ___ / 40
  1. 1.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  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) 8 (b) 16 (c) 12 (d) 6
  3. 3.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 105 (c) 210 (d) 120
  4. 4.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 56 (d) 28
  5. 5.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 36 (c) 18 (d) 21
  6. 6.There are 4 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) 40 (b) 24 (c) 9 (d) 20
  7. 7.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 28 (d) 49
  8. 8.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  9. 9.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) 48 (b) 11 (c) 32 (d) 24
  10. 10.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
  11. 11.6 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) 11 (b) 60 (c) 36 (d) 30
  12. 12.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 16 (c) 12 (d) 6
  13. 13.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 18 (c) 81 (d) 72
  14. 14.5 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) 7 (b) 15 (c) 20 (d) 10
  15. 15.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 42 (c) 49 (d) 14
  16. 16.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 182 (c) 196 (d) 105
  17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  18. 18.5 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) 30 (b) 15 (c) 20 (d) 8
  19. 19.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 15 (d) 12
  20. 20.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 81 (d) 45
  21. 21.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  22. 22.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) 10 (b) 48 (c) 24 (d) 28
  23. 23.4 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) 16 (b) 24 (c) 7 (d) 12
  24. 24.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 24 (c) 11 (d) 32
  25. 25.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 90 (c) 45 (d) 100
  26. 26.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 28 (d) 64
  27. 27.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 120 (c) 225 (d) 210
  28. 28.There are 5 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) 20 (b) 8 (c) 30 (d) 15
  29. 29.There are 8 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) 15 (b) 64 (c) 112 (d) 56
  30. 30.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  31. 31.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  32. 32.4 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) 48 (b) 28 (c) 24 (d) 10
  33. 33.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  34. 34.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 42 (d) 49
  35. 35.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 100 (d) 45
  36. 36.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 35 (c) 70 (d) 42
  37. 37.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  38. 38.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 30 (d) 15
  39. 39.3 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) 9 (b) 6 (c) 12 (d) 18
  40. 40.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 40 (c) 24 (d) 20

Answer key

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

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